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Effects of a formulary expansion of the use of SSRIs and health care services by depressed patients in the California Medicaid program

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Effects of a formulary expansion of the use of SSRIs and health care services by depressed patients in the California Medicaid program

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Content Effects of A Formulary Expansion on the Use of SSRIs and Health Care Services by Depressed Patients in the California Medicaid Program by Lizheng Shi A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHARMACEUTICAL ECONOMICS AND POLICY) May 2001 Copyright 2001 Lizheng Shi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UM1 Number: 3 0 2 7 7 7 7 Copyright 2001 by Shi, Lizheng Ail rights reserved. ___ ® IJM J UMI Microform 3027777 Copyright 2002 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Beil & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UNIVERSITY OF SOUTHERN CALIFORNIA The Graduate School University Park LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, w ritten b y L f'zJie-riJ _ U nder th e direction o f h..kL. D issertation Com m ittee, and approved b y all its members, has been p resen ted to an d accepted b y The Graduate School, in p a rtia l fulfillm ent o f requirem ents fo r th e degree o f DOCTOR OF PHILOSOPHY D ean o f Graduate Studies D ate M ay 11, 2001 DISSER TA TION COMMITTEE Chairperson R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Lizheng Shi Jeffery S. McCombs ABSTRACT EFFECTS OF A FORMULARY EXPANSION ON THE USE OF SSRIS AND HEALTH CARE SERVICES BY DEPRESSED PATIENTS IN CALIFORNIA MEDICAID PROGRAM Background: Fluoxetine and paroxetine were added into the California Medicaid (Medi-Cal) formulary in May 1996. This formulary expansion (FE) encouraged both the expansion of drug therapy for depression [access effects (AEs)] and substitution of the added drugs for conventional antidepressants [substitution effects (SEs)]. Objectives: This study investigated the effects of the FE on the process of treatment selection, corrected for potential treatment selection bias due to the AEs and SEs in the models of post-treatment costs, and compared costs before and after the FE and across alternative drugs. Methods: 6,409 patient-treatment episodes for major depression (MDD) were identified. The comparative costs before and after the FE, and between the alternative antidepressant and no antidepressant therapy were analyzed using multivariate statistical models. Treatment selection bias due to AEs and SEs created by the FE were controlled for in the health care costs models using a double selection bias methodology. Results: AEs and SEs due to the FE increased the likelihood that patients received either fluoxetine in the post-FE period (odds ratio=9.44 p<0.001), or paroxetine (odds ratio = 17.8 p<0.001) while decreasing likelihood of using the TCAs (odds ratio=0.59 p<0.001) relative to the no-drug therapy population. Significant selection bias due to R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. unobserved variables created by the SEs was found in TCAs costs model, while the selection bias due to the AEs was found in fluoxetine costs model. However, neither AEs bias nor SEs bias was found to be significant in paroxetine costs model. Antidepressant therapy using available antidepressants displayed increased savings in total health care costs after the FE relative to the untreated population. Conclusions: The FE had an unevenly distributed impact on the initial therapy selection process that had an impact on the health care costs in terms of the AE and SE selection bias. Moreover, fluoxetine differentiated from paroxetine in the pattern of AE and SE selection bias. The overall costs of treating depression did not increase with expanded access to the more expansive antidepressants. Word Count: 346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Dedication To my family, for their love and support -- Ls. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE OF CONTENTS Chapter 1. Introduction — 1 LA. Policy Context for Adding Fluoxetine and Paroxetine to the California Medicaid Drug Formulary — 1 l.B. Supporting Evidence for the Formulary Expansion — 1 l.C. Statistical Challenges on Assessing Formulary Policy Impact — 5 l.C .l. Historical Factors Affecting Medi-Cal Program — 6 l.C.2. The Substitution effects — 7 1 .C.3. The Access effects: Intended and Unexpected Effects -8 1.C.4. Statistical Challenges of Modeling Access effects and Substitution effects --10 1.D. Objectives of Assessment for the Formulary Expansion — 13 2. Treatment Selection With Alternative Selection Rules — 16 2.A. Introduction — 16 2.B. A Survey on Treatment Selection Models -1 8 2.B.I. Introduction — 18 2.B.2. Selection Rules for Standard Lee’s Method -1 9 2.B.3. Two-Stage Estimation for Single Lambda Method -21 2.B.4. Expansion of Single-Stage Selection Rule to Untreated Population -2 3 2.C. Double Lambda Method -2 5 '2.C.I. Introduction for Treatment Selection with Multiple Choice Criteria — 25 2.C.2. Selection Rule For Double Lambda Method — 26 2.C.3. Two-Stage Estimation Method for Double Lambda Method — 34 2.D. Comparative Cost Effects across the Alternative Antidepressants — 36 3. Formulary Policy Impact on SSRIs Use and Health Care Costs -3 9 3.A. Data and Primary Outcomes -3 9 3.A.I. Data -3 9 3.A.2. Exclusion and Inclusion Criteria for Study Sample -3 9 3.A.3. Outcome Measure: Health Care Costs — 42 3.B. Model Specification — 43 3.B.I. Common Variables Shared by Choice Model and Cost Model -4 3 3.B.2. Model Specification Test — 43 3.B.3. Final Model Specification — 46 3.C. Results -4 6 3.C.I. Descriptive Statistics -4 6 3.C.1.L Subjects and Changes in the Number of Patient-Episodes — 46 3.C. 1.2. Prior Health Care Costs before and after the formulary Change-51 3.C.2. Double Lambda Method versus Single Lambda Method — 54 3.C.2.I. Factors Influencing the Treatment-drug Choice -5 4 3.C.2.2. Calculate Treatment Selection Correction Terms — 59 3.C.2.3. Treatment Selection-Corrected Log Total Costs Models -61 3.C.2.3. 1. The Impact of Treatment Selection Bias on Total Health Care Costs -61 3.C.2.3.2. Impact of Treatment Selection Bias on Other Parameter Estimates -7 2 3.C.2.4. Influence of Heteroscedasticity on Double Selection Bias in Total Health Costs Models — 74 3.C.2.5. Double Selection Bias in Cost Models by Type of Service — 77 3.C.2.6. Comparative Logarithm Transformed Cost Effects By Type of Service across the Alternative Drugs Relative to No Therapy -7 8 iii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.D. Discussion — 83 3.D.I. Methodological Issues -8 3 3.D.2. Impact of the Formulary Expansion on Two-Stage Treatment Selection Process and Parameter Estimates for Total Health Care Costs Models -8 9 3.D.3. Policy Implications of Adding Two SSRIs to the Medi-Cal Formulary — 92 3.D.4. Limitations of This MDD Study -9 4 3.E. Conclusions — 97 Reference — 99 Appendix — 106 iv R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Figures Figure 2.B.I. Drug Choice among the Treated Patients -2 0 Figure 2.B.2. Drug Choice among the Depressed Patients (Treated and Untreated) — 24 Figure 2.C.I. Selection Process for Two-Stage Treatment-drug Choice Model — 27 Figure 3.C.I. Antidepressant Episode by Drug Types in the California Medicaid Program -4 9 Figure 3.C.2. Health Care Costs in Prior-Treatment Period by Type of Service before and after the Formulary Expansion among TCAs Users -5 2 Figure 3.C.3. Health Care Costs in Prior-Treatment Period by Type of Service before and after the Formulary Expansion among Paroxetine Users -5 2 Figure 3.C.4. Health Care Costs in Prior-Treatment Period by Type of Service before and after the Formulary Expansion among Sertraline Users — 53 Figure 3.C.5. Health Care Costs in Prior-Treatment Period by Type of Service before and after the Formulary Expansion among Fluoxetine Users -5 4 List of Tables TABLE 3.C.I. Study Sample (N=6,409) by Initial Antidepressants -4 8 TABLE 3.C.2. Baseline Characteristics of Each Initial Antidepressant Group -51 TABLE 3.C.3. The Coefficient Estimates and Their Corresponding Odds Ratio of Treatment -Drug Choice Model Estimated by Two-Stage Multinomial Logit Method -5 7 TABLE 3.C.4A. Actual and Predicated Probability for Each Alternative Antidepressant Group before and after the Formulary Change -5 9 TABLE 3.C.4B. Correlation of Coefficients between the Decision to Seek Treatment and the Alternative Drug Choice before and after the Formulary Expansion -61 TABLE 3.C.5A. Estimates of Log Total Costs Equation for the TCAs Users (N=l,281) -6 4 TABLE 3.C.5B. Estimates of Log Total Costs Equation for the Fluoxetine Users (N=1,003) — 66 TABLE 3.C.5C. Estimates of Log Total Costs Equation for the Paroxetine Users (N=947) — 68 TABLE 3.C.5D. Estimates of Log Total Costs Equation for the Sertraline Users (N=306) — 69 TABLE 3.C.5E. Estimates of Log Total Costs Equation for the HCAs Users (N=l,308) — 70 TABLE 3.C.5F. Estimates of Log Total Costs Equation for the Other AD Users (N=279) -71 TABLE 3.C.6. Influence of Heteroscedasticity on Parameter Estimates of Total Health Care Costs Models by Drug Type — 76 TABLE 3.C.7. Treatment Selection Bias on Health Care Cost Models by Drug Type and by Type of Service in California Medicaid Program -7 8 TABLE 3.C.8. Comparative Cost Effects of Alternative Initial Drugs with Single Lambda Adjustments before/after the Formulary Expansion by Type of Service (No Antidepressant Therapy as the Comparison Group) -8 0 TABLE 3.C.9. Comparative Cost Effects of Alternative Initial Drugs with Double Lambda Adjustments before/after the Formulary Expansion by Type of Service (No Antidepressant Therapy as the Comparison Group) -8 2 v R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1. Introduction LA. Policy Context for Adding Fluoxetine and Paroxetine to the Medi-Cal Drug Formulary Drag formularies theoretically provide the foundation for guiding clinicians in choosing the safest, most effective, and least costly agents for treating particular medical problems. However, intended and unexpected consequences may result from any formulary expansion. As a result, policy makers are well advised to evaluate the effectiveness of the newly added medications on health care costs as a formulary expansion may have altered drug use patterns, including the possibility of inappropriate use of the newly added drags after the formulary expansion. California Medicaid (Medi-Cal) program required prior-authorization for all selective serotonin-reuptake inhibitor (SSRI) antidepressants prior to May 1996. Paroxetine and fluoxetine were added to Medi-Cal’s formulary at that time based on available data documenting the efficacy and effectiveness of SSRI antidepressants relative to conventional tricyclic antidepressants (TCAs). Since the addition of these two antidepressants to the Medi-Cal prescription drug formulary, the depressed Medi- Cal beneficiaries have had unrestricted access to these two SSRI antidepressants when used as the initial drags. This study evaluates the impact of this formulary expansion on the treatment of depressed patients before and after this formulary expansion. l.B. Supporting Evidence for the Formulary Expansion Information regarding the prevalence of treated and untreated psychiatric disorders in the population is an important factor for guiding public health policy. l R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Depression is a common, debilitating psychiatric disorder (Kessler et al. 1994). Major depressive disorder has a lifetime prevalence of 17% and a 12-month prevalence of 10% (Saklad, 1995). This suggests that approximately 20 million adults in this country experience an episode of major depressive episode each year. The 6-month prevalence for selected DSM-III major depressive disorder is 2.2%-3.5% in 3 different communities in the United States (Myers et al. 1984). At any point in time, the prevalence ranges from 2.6%-6.2% of the general population (Angst, 1992). Major depression (MDD) is the most common clinical problem seen in primary care and is the most prevalent in patients with chronic medical illness (Angst, 1992). Prevalence of significant depressive symptoms is estimated at 20.9% for patients seeking medical treatment but only 1.2% of patients cited depression as the purpose for seeking treatment (Zung et al. 1993). Health policy makers are seeking ways to improve clinical, economic, and humanistic outcomes for patients with depression. Depression is a serious disorder that is associated with significant morbidity and a high mortality rate from suicide (Regier et al. 1988). The depressed patients consume significant amounts of medical, psychiatric, and pharmacological resources and also significantly and indirectly cause the societal loss due to depression-related suicide and low productivity (Greenberg et al. 1993; Le Pen et al. 1994). It has been estimated that the cost of depression in 1990 was approximately $43 billion in the United States (Greenberg et al. 1993). Of this total, 27% ($12.4 billion) was attributable to the direct medical costs with inpatient medical care being responsible for the majority of direct medical costs. Health care 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. costs for primary care patients with recognized depression were estimated at $4,246 per year versus $2,371 per year for non-depressed patients and the increased health care costs were manifested as higher cost for every category of care: primary care, medical specialty, medical inpatient, pharmacy, and laboratory (Simon et al. 1995). A comparison of depressed hospitalized patients having a variety of physical illnesses to a matched nondepressed group having the same primary diagnosis-related groups (DRGs) and severity of illness demonstrated that the depressed group has an increased length of inpatient stay by 10 days in average (Verbosky et al. 1993). In both cross- sectional and longitudinal studies, depression has been associated with limitations in well-being and functioning that were equal to or greater than those of patients with chronic general medical conditions such as diabetes and arthritis (Wells et al. 1989; Hays et al. 1995). Depression is one of the most treatable mental health disorders in both psychiatric and general health care settings (Eisenberg, 1992). Approximately two- thirds of patients with major depression respond dramatically to acute antidepressant therapy. However, compliance with antidepressant therapy has been poor due to the side effect profile of older TCAs (McCombs et al. 1990). Fortunately, available antidepressant medication options have multiplied over the past 15 years with the advance of a new generation of SSRI antidepressants. Previous studies have identified a few facts and several ways in which the availability of the SSRIs has affected the treatment of depression. First, the SSRIs have better safety profile and patient tolerability than the TCAs (Preskom et al. 1995; 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Freemantle et al. 1994; Montgomery et al. 1994; Anderson et al. 1995). Second, an increase in the number of antidepressant prescriptions has been observed, mostly due to increased use of the SSRIs (Sclar et al. 1998; Donoghue et al. 1996). The superiority of SSRIs over TCAs in efficacy, effectiveness and safety data has gradually led to the acceptance of first line treatment using SSRIs. Third, the patients on SSRIs experienced lower health care costs than patients on TCAs (Sclar et al. 1994; Skaer et al. 1995; McFarland, 1994; Bentkover and Feighner, 1995). With the emergence of the SSRIs, physicians and formulary managers have begun to compare the effectiveness of alternative products within this class. Significant differences in the pharmacokinetic profiles, side effects, and efficacy data between the SSRIs have been found (DeVane, 1994; Preskom 1995; De Wilde et al. 1993; Bennie et al, 1995; Ernest et al. 1995). However, it is unclear how these differences can be translated into differences in health care costs. A number of recently published studies using retrospective administrative data have compared direct medical costs for depressed patients conditional on three leading SSRIs, fluoxetine, paroxetine, and sertraline (Hylan et al. 1998; Russell et al. 1999). No consensus has been reached on the cost comparisons among these three SSRIs. In Hylan et al study, the 1-year total direct health care costs were found to be statistically significantly lower for patients initiating therapy on fluoxetine than for patients initiating therapy on a TCA or sertraline. The findings in Hylan et al study suggested that total direct health care costs differed across initial antidepressant selection. In 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Russell et al study, however, no statistically significant difference was found across the SSRIs. A study (McCombs et al. 1999) based on the Medi-Cal 5% short claims data justified the initiative of adding fluoxetine and paroxetine in the Medi-Cal’s formulary. In the Medi-Cal program, nearly 80% of patients treated with the TCAs for depression failed to complete 6 months of uninterrupted drug therapy above minimum therapeutic doses. Interrupted or terminated therapy was found to increase total health care costs per patient in the first post-treatment year. However, fluoxetine was associated with significantly lower overall health care costs and significantly higher completion rate compared with TCAs, sertraline, and paroxetine. However, these results must be interpreted with caution given the relatively small number of patients treated with each of these three SSRIs found in this Medi-Cal data and the relatively short time for which paroxetine and sertraline were available to Medi-Cal patients (i.e., launch bias) during its study period (1987-1996). It is possible to re-assess the impact of the alternative antidepressants on health care costs by analyzing Medi-Cal data from a more recent period when these three leading SSRIs have became established agents. In addition, the issue of comparative health care costs must be addressed in light of the influence of the formulary expansion to extend the coverage of two SSRI antidepressants. l.C. Statistical Challenges on Assessing Formulary Policy Impact All research studies designed to estimate the impact of government policy initiatives over time face three important statistical challenges. First, the analysis must 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. take into account exogenous historical factors that may have also affected the outcomes under investigation during the study period (1994-1998). These historical factors are a common threat to the internal validity of all studies that measure the impact of policy changes without a parallel population that was not affected by the policy initiative. Second, the analysis must be careful to disentangle the multitude of ways that the policy initiative may have affected the system under study. Of particular importance in policy analysis are possible unexpected effects that must be explicitly accounted for in the analysis. Finally, if alternative treatment options are to be compared, the analysis must account for possible treatment selection bias. In the case of a formulary expansion, the treatment process itself will be affected by better access to new therapies. Since historical factors, possible unexpected access effects and treatment selection bias may play important roles in this analysis, the specifications of the statistical models were carefully constructed to attempt to control for these factors. Moreover, the hypotheses to be tested in this study were carefully crafted to clearly account for both intended and unexpected effects. l.C.l. Historical Factors Affecting Medi-Cal Program During the study period the Medi-Cal program experienced significant exogenous changes, some of which were unrelated to the treatment of depression or the formulary expansion. First, an improved economy provided expanded opportunities for able-bodied welfare recipients to return to work. At the same time, welfare reform limited the time that able-bodied recipients could receive welfare and coverage under the Medi-Cal program. As a result, the Medi-Cal program 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. experienced a steady decline in the number of eligible recipients over the study period. Second, a concurrent health policy initiative was implemented aimed at enrolling non disabled Medi-Cal recipients into managed care programs. This initiative decreased the total number of Medi-Cal recipients who received services in the fee-for-service sector from which the data for this study were derived. Both factors were likely to affect the characteristics of the population of MDD patients seeking treatment over the course of this study. However, it is unclear how these changes in the patient population would affect the likelihood that a patient would achieve an adequate course of antidepressant therapy, the impact of completed therapy on direct health care costs or the impact of alternative medications on costs. I.C.2. The Substitution Effects The expansion of the Medi-Cal formulary to include fluoxetine and paroxetine was primarily intended to cause a substitution of these medications for TCAs and heterocyclic antidepressants (HCAs) in the treatment of MDD patients. However, the impact of potential substitution effects on treatment outcomes and costs depend on the characteristics of the patient population switched to the added SSRIs. Assuming that more severely ill and more difficult to treat patients were switched from conventional medications to the added SSRIs, the following differences in drug therapy outcomes and post-treatment costs should be observed after the formulary expansion: (1) The effectiveness of antidepressant drug therapy using conventional drugs, as measured by the difference in one-year post-treatment costs relative to the untreated patients, as defined by the MDD patients without 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressant therapy, should improve in the post-expansion period due to the shift of more severely ill and hard to treat patients to the added SSRIs. (2) The effectiveness of the added SSRIs compared to untreated MDD patients should diminish unless these medications prove to be significantly more effective in treating the substitution population. Alternatively, it is possible that the substitution effects included patients who would have responded well to the less expensive medications (i.e., unexpected substitutions). Then the above hypothesized substitution effects will be altered if unexpected substitutions were induced by the formulary expansion. I.C.3. The Access effects: Intended and Unexpected Effects The expansion of the Medi-Cal formulary was intended to improve access to two SSRI antidepressants, paroxetine and fluoxetine, by removing prior authorization requirements that existed previously for all SSRI antidepressants. However, the improved access to two SSRI antidepressants could alter the use of antidepressant drug therapy in both intended and unexpected fashion. Firstly, treatment refractory patients may be encouraged to seek treatment once better medications became available, even though these patients still met the criteria for prior authorization. The intended access effect patients are likely to be more severely ill and less compliant with drug therapy than average. Secondly, however, the removal of prior authorization restrictions may have also had an unexpected access effect. Specifically, prior to the expansion of the formulary, physicians may have been reluctant to treat less severely depressed patients and patients with an uncertain MDD diagnosis with R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the available antidepressants due to their side effect profiles and other risks. Indeed, a “wait and see” strategy may have been adopted and no MDD diagnosis recorded. Many of these patients may have experienced a reduction in symptoms and never returned for further MDD treatment. After gaining access to the selected SSRIs, physicians may have altered the criteria of initiating drug therapy for depression, especially treating patients empirically with an added drug. These access effect patients are likely to be less severely ill and, therefore, also less likely to comply with antidepressant drug therapy over an extended period of time and less costly to treat in the post-treatment period. Given the heterogeneity of the access effect population, it is hard to‘ predict the impact of the access effects on treatment costs in the post-expansion period. Refractory patients and patients previously unwilling to use antidepressants are also likely to exhibit higher than average post-treatment costs, while patients suffering from less severe forms of depression are likely to be less costly than the average depressed patient treated prior to the formulary expansion. If the intended access effect dominates, then the post-treatment costs for patients treated with fluoxetine and paroxetine in the post-expansion period should increase relative to patients treated with TCAs in the pre- or post-expansion period. If the unexpected access effect dominates, fluoxetine and paroxetine patients in the post-expansion period may exhibit lower treatment costs relative to TCAs due to the influx of relatively inexpensive patients into treatment, even if these drugs are not more effective than conventional antidepressants. Unfortunately, it is not possible to completely separate the intended 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. and unexpected access effects, especially in the case of refractory patients returning to treatment versus truly new drug therapy patients starting treatment as a result of changes in the physicians’ treatment criteria. I.C.4. Statistical Challenges of Modeling Access effects and Substitution effects The access effects and substitution effects of this formulary expansion created statistical challenges that must be accounted for separately but with some attention paid to the inter-related characteristics of the access effects and the substitution effects. Conceptually, the implications of statistical challenges can be discussed in three situations with increased degrees of complexity. First, assume that the formulary expansion did not cause some MDD patients, who had not been treated with antidepressants before the formulary expansion, to seek treatment in post-expansion period. In this case, the formulary expansion only resulted in a constant population of treated MDD patients’ changing their choice of alternative antidepressants. Since this constant treated patient population was only influenced by the substitution effects, a single-stage selection adjustment model is sufficient to model the effect of the formulary expansion on the treatment decision process (Heckman, 1979; Lee, 1983; Hylan et al. 1998). Next, assume that the formulary expansion resulted in the access effects, that is, the MDD patients, who previously were not treated with any antidepressant, now select drag therapy as their treatment option. Assume further that this shift of the access effect patients did not change the overall drug selection pattern purely caused by the substitution effects. Under these restrictive assumptions, the access effects are 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. independent of the substitution effects and all alternative treatment options including the non-antidepressant therapy option follows the rule of the independence of irrelevant alternatives (Greene, 1997). That is, the drug choice process can be expanded to include an independent non-antidepressant therapy option and the single- stage bias adjustment model applied to the entire MDD patient population (Section 2.B.4). In reality, the formulary expansion is thought to have resulted in the access effects caused by a change in decision whether or not to use antidepressant therapy and the substitution effects by a change in drug selection rules. Moreover, the access and substitution effects are not independent. The access effect patients would be likely to use one of the two added SSRIs as it is the availability of the added SSRIs that induced depressed patients and/or physicians to select drug therapy option. This interaction between the access effects and substitution effects due to the formulary expansion raised challenges to the statistical models based on a single-stage selection process. The interdependence between the access effects and the substitution effects must be addressed in the statistical methods based on a dual selection structure as proposed in the statistical methods (Section 2.C). The access effects may be further complicated if the formulary expansion changed the physician’s willingness to record an MDD diagnosis after prescribing the added SSRIs to a patient not previously considered for antidepressant therapy. Sometimes a recorded MDD diagnosis did not lead physicians to prescribe antidepressants for some MDD patients, who thereby were defined as new-entry of 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. untreated patients. Under both conditions, it is not possible to identify these actual but “under-diagnosed” MDD patients in the period prior to the formulary expansion. This lack of data in the prior-expansion period makes it ever more important that the analysis uses statistical methods that document the extent to which the access effects and the substitution effects existed after the expansion of the Medi-Cal formulary in May 1996. On one hand, the extent to which the formulary expansion induced the intended access effects should be observable as a drop in the number of MDD patients initiating episodes of treatment without antidepressant therapy. The unexpected access effect would appear as an increased fluoxetine and paroxetine users without a corresponding drop in untreated MDD patients, which would be unreliable to differentiate from the intended access effect given the possibility for new-entry of MDD patients with no antidepressant use. Indeed, both intended and unexpected access effects would appear as an increase in the likelihood (odds ratio) of using two added SSRIs relative to no antidepressant therapy. The data for health care utilization or clinical characteristics prior to the episode might provide some indirect and limited evidence to distinguish the two components of the access effects. The impact of the formulary expansion on the substitution effects should be observable as a drop in the number of MDD patients using TCAs and/or HCAs as the initial drug with corresponding increase in the number of fluoxetine and paroxetine patients. Similarly, the substitution effects for these classes of antidepressants can be measured by the change in the odds ratio of using these antidepressants relative to TCAs. 12 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. On the other hand, although both the access and substitution effects could be measured by the changes in the number of patient episodes, both effects could also be viewed as the changes in some unobservable patient characteristics, such as disease severity, compliance with therapy, and etc. Because of the non-randomized choices in treatment selection process, these unobservable factors could also influence the treatment costs in the first year following the initial drugs. The correlation of these unobservable factors between treatment selection and treatment costs results in the treatment selection bias in modeling health care cost. As a result, to compare the health care cost across the alternative drugs, the impact of treatment selection bias related to the access effects and the substitution effects must be taken into account for modeling the health care costs. I.D. Objectives of Assessment for the Formulary Expansion The first objective of this study was to model the effects of the formulary expansion to include fluoxetine and paroxetine on the treatment selection process in patients with major depression diagnosis in their paid claim file. The antidepressant therapies included in this study are fluoxetine, sertraline, paroxetine, HCAs, TCAs and other new antidepressants. In addition, this study also includes MDD patients who do not take any antidepressant. The impact of the formulary expansion on decisions of whether or not to treat a patient and which antidepressant to prescribe was estimated using a two-stage multinomial treatment-drug choice model. Accordingly, the access effects will be attributed to the effects of the formulary expansion on the decision to 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. seek treatment (treatment initiation) and substitution effects will be attributed to the choice of a particular drug (drug choice). The second objective of this study was to measure the extent to which the access effects and the substitution effects of the formulary expansion introduced treatment selection bias into the models of the post-treatment costs. Specifically, the formulary expansion affecting both treatment initiation and drug selection is expected to alter both the observable and unobservable patient characteristics that created the treatment selection bias. This study developed a statistical method to account for two forms of treatment selection bias related to the formulary expansion: treatment initiation (access effects) bias and drug choice (substitution effects) bias. Treatment selection bias was adjusted according to an above discussed two-stage treatment-drug choice process, which allowed researchers to better disentangle the impact of the access effects and substitution effects on health care costs. The utility of this method using a two-stage treatment-drug selection was compared with the estimators adjusted for treatment selection bias under the alternative rules of single-stage selection process, and was also compared with the estimators using standard ordinary least square (OLS) methods. The third study objective was to compare the 1-year post-treatment direct health care costs following initial antidepressant selection for one of the available antidepressants: TCAs, HCAs, fluoxetine, paroxetine, sertraline, and other antidepressants. This comparative cost study must take the potential treatment selection bias into account as well. It is important to continue to examine patients’ 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. direct health care costs that follow initial antidepressant selection using retrospective data from actual clinical practice for at least two reasons. First, previous analyses were conducted in an environment in which the dynamics of treatment selection may differ due to formulary restriction on the SSRIs. A similar study using Medi-Cal data before 1996 (McCombs et al. 1999) covered the period subject to the impacts of both the prior authorization requirement and the launch bias. Second, treatment selection bias in administrative data must be addressed in any study assessing the health care cost across alternative drugs. In this study, the formulary expansion changed the treatment selection pattern. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2. Treatment Selection with Alternative Selection Rules 2.A. Introduction Studies using administrative data (e.g., Medi-Cal paid claims data) to evaluate policy impacts or treatment outcomes have been widely criticized because of their failure to control for selection bias (Anderson, 1994). In this case study, the selection of an antidepressant as initial therapy in clinical practice is not a random process, creating significant opportunity for bias (Rosebaum, 1991). The determinants of antidepressant selection include, but are not limited to, individual disease severity, physicians’ previous experiences and prescribing preferences, prior compliance, prior medication use, and'the range of antidepressants available without the drug formulary restriction. Treatment selection bias, which results from the non-random selection of drug therapies, leads to erroneous inferences about policy impact or treatment outcomes in analytical models. In addition, the treatment selection might be significantly altered by the change of Medi-Cal drug formulary. It is expected that the addition of fluoxetine and paroxetine on the formulary may have substantially changed the treatment selection process by two ways, the access effects and the substitution effects. Specifically, more patients would start their antidepressant therapy because of the improved access to two SSRI antidepressants. The physician/patient’s selection of an antidepressant would change, even for patients who would have been treated prior to the formulary expansion. In other words, the medication treatment from the old antidepressants would be converted to the new SSRIs, especially for those more severely ill patients. As a result, the non-random selection processes between 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. alternative antidepressant therapies and its dependence on the formulary expansion necessitate the application of the methods for correction for treatment selection bias. Ideally, unbiased comparisons of health care costs across alternative antidepressants can be achieved if all possible confounders are measured and used in the analytical models. However, not all aspects of the treatment decision process can be directly observed/measured, especially when using administrative data. If unobservable determinants affecting the treatment decision are also correlated with health care costs, then controlling for the observable characteristics, such as age, gender, prior health service use, prior number of episodes and the like is not sufficient to adjust for'treatment selection bias in modeling health care costs. In other words, treatment selection bias arises when these differences in treatment selection may also affect future health care costs, thus creating a statistical challenge to accurately model the effects of the alternative products on the total health care costs. Failure to include an adjustment for the unobservable variables will lead to incorrect inference (direction, magnitude, and significance level) of the parameter estimates for the observable variables in heath care cost models. This is particularly troublesome when attempts to evaluate the alternative products are subject to the effects of the policy change to expand the drug formulary since this formulary expansion was designed to affect patients’ treatment decision process. The ability of estimate and test econometric models over nonrandom treatment selection is unquestionably one of the most significant innovations in econometrics. Since James Heckman’s seminal work on treatment selection bias (Heckman, 1979), 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the economics literature has abounded with empirical applications employing his proposed methodology. Despite its wide applicability the model initially considered by Heckman had a rather limited selection structure (i.e., dichotomous choice) and was highly parameterized (i.e., normal distribution of model error terms). Subsequent papers, however, have extended it by incorporating different selection rules (e.g., polychotomous choice (Lee, 1983), or two-by-two sequential/joint choice (Danzon andLillard, 1982)) or by employing semi- and non-parametric estimation methods (Vella, 1997). 2.B. A Survey on Treatment Selection Models 2.B.I. Introduction Heckman’s method can be applied in any standard environment of binary choice associated with social programs such as women labor force participation, unionism, and job training programs (Heckman and Smith, 1995). The potential role of Heckman’s method in health service research has been demonstrated in a case study of modeling the effect of antidepressant therapies on medical expenditure for physician services (Crown et al. 1998). In that case study, the treatment selection model yielded very different conclusions regarding the treatment effects of alternative antidepressants than the traditional ordinary least squares regression. In general, clinicians and patients face multiple options rather than a single binary choice. In health service research, treatment selection method associated with polychotomous choice was first introduced in a study of professional income relating to occupational choices between general practice, specialist, and other health 18 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. occupations (Hay, 1980). As a refinement of Hay’s work, a more general method was introduced to account for treatment selection bias of polychotomous choice (Lee, 1983). Health outcomes researchers adopted Lee’s model in evaluating the overall effects of alternative antidepressants on health care costs in the first post-treatment year (Hylan et al. 1998), with log-transformed cost data to control for data skewing. In the choice set of antidepressants, Hylan included 4 different drugs, TCAs, fluoxetine, paroxetine, and sertraline. In addition to the findings of comparative costs across the alternative drugs in Hylan’s study which has been discussed in the section 1.B, it was also found that there was statistically significant treatment selection bias associated with patients using fluoxetine as the initial drug. 2.B.2. Selection Rules for Standard Lee’s Method In order to apply the standard Lee’s Method in this 100% Medi-Cal sample, all untreated MDD patients were excluded from the study population. The selection rule in this MDD study followed the Lee’s method for the correction for selection bias and modified the Hylan’s choice set by adding two more options (i.e., HCAs and other new antidepressants). Therefore, the drug selection in the treated patients can be illustrated in figure 2.B.1 as a choice set of 6 options: TCAs, HCAs, fluoxetine, paroxetine, sertraline, and other new antidepressants. The patients on TCAs were treated as the reference group. The alternative antidepressants were denoted as: fluoxetine=f, paroxetine=p, sertraline=s, HCA=h, and other antidepressants=o. 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 2.B.I. Drug Choice among the Treated Patients Treated Patients T C A s ^ ”"" Fluoxetine Paroxetine Sertraline HCAs Other ADs (0 (P) (s) (h) (o) The effect of this formulary expansion on the choice of initial antidepressant therapy and the first year total health care costs conditional upon initial antidepressant selection can be modeled in the following equations: (2.B.1) l n ( i ^ ) = f lJX1+ £ < iD + eu P(TCAs) (2.B.2) ta(Y2 ,) = A /X 2 + M + ^ In the above two equations, j is assigned as f, p, s, h, and o for an unordered polychotomous antidepressant choice (i.e., choice of initial drug for antidepressant therapy). D is 1 if initiating therapy after the formulary expansion and D is 0 otherwise. J3 id j is the estimated effect of the formulary expansion on the choice of the particular drug j. As a choice model, Equation (2.B.1) describes the process of the drug choice in the treated patients. The dependant variable is the log likelihood ratio, which in this case study is the ratio of the likelihood to choose the specific initial antidepressant Yij (e.g., Yif=l for fluoxetine users) relative to that to choose TCAs, and Xi is a set of determinants for initial antidepressant selection. D is the formulary expansion policy R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. dummy to estimate pdj, the effect of the formulary expansion on the initial antidepressant selection. In Equation (2.B.2) modeling health care costs (i.e., outcome/cost model), the dependant variable is measured as the logarithm transformed total direct health care costs Yij, and X2 is a set of explanatory variables for modeling health care costs. The model specification restriction in Xj and X2 will be discussed in the section 3.B, which in general requires that at least one element of Xi is not present in X2 . The dummy variable for the formulary expansion is not included in the cost equation, which guarantees meeting the requirement for model specification restriction because at least one variable D only exists in the choice model. In contrast to the ordinary least square (OLS) model, this cost model, showed as Equation (2.B.2), has an additional regression term X, the inverse Mill’s ratio (IMR). The IMR is a calculated adjustment factor to control for the influence of unobserved factors. The need for X (lambda) stems from the notion that each initial antidepressant category may comprise of treatment selections due to unobserved factors. The sign of 5 measures the direction of the impact of unobserved factors and the inference of 5 determines the significance of selection bias. Because the standard Lee’s method is only involved in one X term in the cost equation, the standard Lee’s method thereby is defined as single lambda method. 2.B.3. Two-Stage Estimation for Single Lambda Method The estimation for the single lambda model proceeds in two stages. First, Equation (2.B.1) is specified as a multinomial single-stage choice model for each of 21 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressant drug categories. The probability of receiving a particular antidepressant thereby is calculated from the estimates in first stage choice equation, Equation (2.B.1). Based on the distribution assumption for the error terms eq, the X term thereby is a function of the calculated probability. Specifically for the fluoxetine users, X fiu o x e tin e can be calculated as (" 1 D O '! h (f)(® \-P fluoxetine^) (2.B.3) ^fluoxetine = --------------‘---------- P fluoxetine In Equation (2.B3), the P fiu o x e tin e is the probability of receiving treatment with fluoxetine in the treated population. The function of < |> and < P are the probability density function (pdf) and the cumulative density function (cdf) of standard normal distribution, respectively. The -§(0>l(p flu o x e tin e ) is the marginal probability of not using fluoxetine as the initial antidepressant therapy. In other words, the X represents the marginal probability of not receiving fluoxetine given that the particular patient is actually on fluoxetine as the initial drug. When the patient is predicted not to receive fluoxetine based upon the observable factors, but he/she fills prescribed fluoxetine, he/she has very large potential for bias. Conceptually, this means that the unobservable factors that are actually responsible for the decision are not accounted for in the study. As a result, the risk of misinterpretation for the effects of explanatory variable X2 on the health care costs might be high when these unobservable factors significantly affect the health care costs as well. 22 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Since the true value of P flu o x e tin e is not known, one must first estimate the choice model to predict the p jiu o x e tm e , then use the predicted value of P fiu o x e tm e to compute the ^ flu o x e tin e for every fluoxetine user according to Equation (2.B.3). In the same way, the X term for all other types of antidepressants can be computed based on the estimates of choice model corresponding to the actual antidepressant prescribed. Therefore, the value for X term is unique to every patient. Second, within each antidepressant group, the parameter estimates for Equation (2.B.2) are estimated by OLS regression, which has the X term as a regressor. The idea of including this adjustment factor X in Equation (2.B.2) to control for treatment selection bias due to the unobservable differences across patients can be intuitively explained as explicit representation of unobservable effects by an estimator from the process of treatment selection. However, this estimation method implicitly assumes that the MDD patients who did not use any antidepressant were identical to the treated patients regarding all aspects of their characteristics and the decision to seek treatment. In addition the formulary expansion also affects the decision to seek treatment, creating the access effects. As a result, the single lambda method has a particular weakness because the real situation does not always follow this implicit assumption as discussed in the statistical challenges of modeling the access effects. 2.B.4. Expansion of Single-Stage Selection Rule to the Entire MDD Population Although depressive disorder is one of the most prevalent and treatable psychiatric diseases, a certain proportion of affected population declined the 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressant therapy. Excluding the untreated population in the analysis missed the access effects of the formulary expansion. In a recent antidepressant study, untreated patients were included in the analysis to examine the possible treatment selection bias related to the untreated patient population (Edgell et al. 2000). This study considered 4 cohorts: no therapy, psychotherapy, drug therapy, and combination therapy. After controlling for both observed and unobserved factors, total health care costs were found to be higher in patients who initiated therapy with drug therapy and combination therapy as opposed to no therapy or psychotherapy. The single-stage selection rule illustrated in Figure 2.B.1 can be expanded to the entire MDD population by adding a choice branch of untreated population as shown in Figure 2.B.2. As a result, the depressed population was broken down into 7 cohorts: TCAs, HCAs, fluoxetine, paroxetine, sertraline, and other new antidepressants as well as the untreated patients (no antidepressant therapy). Figure 2.B.2. Drug Choice among the Depressed Patients (Treated and Untreated) MDD Patients TCAs Fluoxetine ^ Paroxetine Sertraline'*®’ HCAs ^ Other ADs (f) (P) Untreated (st (h) (o) The two-stage estimation procedures used in this expanded population are similar to the method discussed in section 2.B.3. As a matter of fact, the expansion of selection rule to untreated population will just add one more choice branch in the choice set in the first stage multinomial logit choice model. Therefore, it is 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. noteworthy that the p flu o x e tin e in section 2.B.3, which is re-calculated from a single-stage multinomial logit model estimates using the whole MDD population, should be interpreted as the probability of receiving treatment with fluoxetine in the entire depressed population. Accordingly, a new A term is calculated for every MDD patient reflecting his/her treatment selection. The second stage cost models were then re- estimated with new values of the A term for each individual patient. 2.C. Double Lambda Method 2.C.I. Introduction for Treatment Selection with Multiple Choice Criteria When comparing the health care costs associated with the alternative antidepressant used as the initial medication, one should consider how the decisions surrounding antidepressant therapy operate. In medical practice, the vast majority of depressed patients are prescribed a variety of antidepressants ranging from old TCAs to new and expansive SSRIs. However, a proportion of patients may voluntarily decide not to fill their prescribed antidepressants. Other refractory patients may receive other forms of therapies based on their previous medication history. Finally, many less severely ill patients may not have received an antidepressant due to the risk of side effects and limited efficacy of the older products. Obviously, there are two different selection processes at work: whether or not to be treated and which drug to be used, if treated. These two decisions are hierarchic in nature but closely correlated. Moreover, both processes are likely to be significantly affected by the formulary expansion to include two SSRIs. To better account for this sequential treatment 25 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. selection process, a new method to model the selection process and treatment outcome is warranted. As discussed before, formulary expansion might play a significant role in deciding both treatment initiation (access effects) and drug choice (substitution effects). This conjecture bridges the individual adjustment term for either type of treatment selection bias with the corresponding effect of the formulary expansion. 2.C.2. Selection Rule For Double Lambda Method In the whole MDD patient population, a two-stage treatment-drug selection can be formulated following the framework developed by Viverberg (Viverberg, 1993; Viverberg, 1995). Figure 2.C.1 illustrates the decision tree of this sequential treatment-drug choice process. To start, for any depressed patient, the decision to seek treatment is denoted by M with 2 alternatives, either m=l (patient treated with an antidepressant) or m=0 (patient treated with non-antidepressant option). The initial drug choice in treated population is denoted by regimen R, with total 6 alternatives, such that r=TCAs, HCAs (h), fluoxetine (f), paroxetine (p), sertraline (s), and other new antidepressants (o). Total health care costs in state (m, r) are defined as Cm, which is determined by observable characteristics X m r and a disturbance term such that (2.C.1) C nir= Xm rP m r+ {J-m r For a patient treated with a particular antidepressant r, Cir was actually observed only when a person filled a prescription for drug r. For this patient, health care costs 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. associated with other treatment option, Qr* is not observable because of either r** r or m*=0. For an untreated patient, health care costs incurred after the major depression diagnosis, C m r was generalized as Co and actually observed when the diagnosed patient stays in the untreated population. Written in general notation, Cm * r* is not observable given m*^ m or r*^ r. Figure 2.C.I. Selection Process for Two-Stage Treatment-drug Choice Model MDD Patients Treated (m=1) Not Treated (m=0) T C A ^ Fluoxetine Paroxetine Sertraline ^HCA Other ADs (f) (P ) (s) (h) (o) The sequential treatment-drug choice is based on utility comparisons. Utility experienced in state (m, r) depends on health care costs measured by C m r, and patient characteristics captured by Z m r'. (2.C.2) U nu^Zm r+Sm rCm r In Equation (2.C.2), z^- contains systematic components, as determined by the vectors Zm r, and a random component (£z ,m r). Thus we have (2.C.2 ) Umr^ZmrCtmr + £z,m r)+ §m r(% m rP m r + P -m r)— V jrsr+ £m r where V m r represents the combined systematic components (i.e., Zm r and % m r) and £ m r captures the combined random disturbances (i.e., £z > m r and jim r). By assumption, a 27 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. person chooses medication therapy M=m and/or initial drug R=r such that the expected utility Un* is maximized: (2.C.3) (M, R)=(m, r) if and only if U m r >Um * r* for all and/or r**r Note that this model assumes perfect information about all medication therapy and drug choices and ignores dynamic considerations of the drug switching and/or augmentation. It is a model of the initial treatment selection, which can be made with knowledge about re-treatment options for future extension. The model is complete when the distribution of the disturbance terms is specified. To make the model empirically tractable, it is assumed that £ m r has an identical independent distributed (i.i.d.) type I extreme value or Gumbel distribution (Ben-Akiva and Lerman, 1985). The sequential choice model can then be estimated as a two-stage multinomial logit model, which is different from the single-stage multinomial logit model used in Lee’s method. For notational simplicity, the method discussion focuses on a person who chooses fluoxetine in the notation of the choice set {m=l, r=f}. Conditional on the decision of initiating medication therapy, a person chooses to take fluoxetine if (2.C.4) Uif>max (Uir, r?T) The right-hand side of Equation (2.C.4) has a Gumbel distribution with location parameter (2.C.5) Vif'=ln(S r*feV lr) Therefore rewrite the right side of Equation (2.C.4) as V)f '+8 if'. Collecting the disturbance terms and defining remand Am, the drug choice condition is rewritten as 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (2.C.6) T|fii=§if ’ -£if <Vif-Vif =Afii=PfnXfii+pfdiiD In Equation (2.C.6), Xfn are the explanatory variables for choosing fluoxetine and Pfduis the estimated substitution effects of the formulary expansion on choosing fluoxetine relative to TCAs. If defining pm=pif/(pif+2, j*fPir)=F(Afu) as the conditional probability of choosing fluoxetine in the treated group, where F is the logit cumulative distribution function, then pm can be expressed as eA fn r&TCAs Equation (2.C.6) can be reformatted into normal distribution equivalent form r (2.C.7) tln fii=0'1[F(tlf,i)]< ( I> " 1[pfii]= An fu This is the selection condition to choose fluoxetine as initial drug among all alternative drug classes conditional on the decision of antidepressant therapy. Now turn to the decision of treatment initiation. A patient initiates his/her antidepressant therapy (m=l) if (2.C.8) max Uit>U0 The left-hand side of Equation (2.C.8) has a Gumbel distribution with location parameter (2.C.9) Vi=ln( I m = iXreV rl1 ) Therefore the left-hand side of Equation (2.C.8) can be represented as V1+S1 and the right-hand side as V0+8 0 . Again, collecting the disturbance terms, we have (2.C.10) T|i=Eo-8 i<Vi-Vo=Ai=PiXi+PidD 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In Equation (2.C.10), Xi are the explanatory variables for treated patients (in this case, it is for fluoxetine users). We will define the Pid later. If defining pi=pif+X r*fpir as the probability that medication therapy is chosen, and following the same logit model format as Equation (2.C.6’), then pi can be expressed as Equation (2.C.10) is restated in its normal distribution equivalent form as This is the selection condition for a patient to initiate his/her antidepressant therapy Determined by the selection rules in Equation (2.Q.7) and Equation (2.C.11), the two choices are expressed as conditions on normally distributed and correlated distribution assumptions on p.if, the vector (T |n fn, T |\ jin) is now assumed to be jointly normally distributed with covariance matrix: If the decision to seek treatment and the drug choice are independent (this condition will be reconsidered later), by simple probability calculation, the unconditional probability of choosing fluoxetine is (2.C.11) rini=#-1 [F(Tii)]<#-1 [pi]=An1 variables T |"fu and T{\ with a correlation coefficient p. Combined with the normal fan I f-1 P - O (2.C.12) (2.C.13) r^TCAs A fa+ A . r*TCAs 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Following the logic of Equation (2.B.1) on log likelihood function, only the nominator of Equation (2.C.13) carries the information for the effects of the formulary expansion on the selection of fluoxetine relative to no antidepressant therapy, showed in Equation (2.C.13’). (2.C.13’) l n ( ^ ) = A,,, +A = + f lX ,) + (&„„ + P o As mentioned in Equation (2.C.6), Pfdiiis the estimated substitution effects of the formulary expansion on choosing fluoxetine relative to TCAs. Accordingly and intuitively, Equation (2.C.13’) demonstrates that the summation of f 3 f < m in Equation (2.C.6) and Pid in Equation (2.C.10) is the estimated access effects of the formulary expansion on choosing fluoxetine relative to no antidepressant therapy. Obviously all above equations for patients using fluoxetine as the initial drug can be easily extended to other types of antidepressants. More specifically, to better understand the meaning of Pm, Equation (2.C.13) can be extended to the TCAs-treated patients as Equation (2.C.13” ). (2.C.13” ) Plwi=PTCM *p, = (. ‘ = - ** 1 + ^ e A n l + eA l (1 + ]£f?4ll)(l + eA l) r&TCAs r&TCAs Equation (2.C.13” ) intuitively demonstrates that Pm in Equation (2.C.10) is the estimated access effects of the formulary expansion on choosing TCAs relative to no antidepressant therapy. More importantly, the information structure in Equation (2.C.13) and the extensions for all other type of antidepressants such as Equation (2.C.13” ), as well as 31 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the log likelihood function Equation (2.C.13’), provide the foundation to build the likelihood function for estimating the two-stage multinomial logit model. As a result, maximum likelihood estimation (MLE) can be employed to obtain the coefficient estimates J3 rii, P rdii, Pi, and Pid for the patients prescribed an antidepressant r in the two-stage multinomial logit model for a sequential choice processes. Because the decision to seek medication treatment and the type of antidepressant prescribed is likely to be correlated, it is necessary to turn back to solve the correlation coefficient p between rfi andrfV in the above variance-covariance matrix (2.C.12). Both the decision to seek treatment and the drug choice across all alternatives are correlated, if non-zero value of p is found. In other words, the assumption for independence of two-stage selection process is not required in the estimation procedure eventually. In principle p can be calculated from the following equation: (2.C.14) p = J J o - 1[J P(77/ll)]^»-1[^(771)]^(77/ll,/7l)^77/lle /7 7 1 Therefore, Equation (2.C.14) presents an analytical difficulty. There exists no analytical expression for g, nor for O'^Ff.)]. An alternative numerical computation is to employ a Monte Carlo algorithm to estimate p (Viverberg, 1993). In the present MDD study, a similar Monte Carlo algorithm with 1,000 random runs was conducted to obtain the estimated p for each member of the sample: p varies between sample members. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Under the above variance-covariance assumptions in Equation (2.C.12), the health care cost model for a patient treated with fluoxetine can be expressed as the expected value of logarithm-transformed total health care costs In Equation (2.C.15), a^fu and a^iu are the coefficients for the adjustment terms for double selection bias. To simplify the notation for future discussion, a^fu and Oirjia can be also expressed as 0fu and 0i. The two adjustment terms can be calculated as Negative values of 0 ^ and 0 iniu imply positive treatment selection bias. In other words, 0 infu<O or 0 fii<O signifies that the substitution effects, which is associated with the selection of fluoxetine across the available drugs, resulted in higher total costs in these fluoxetine users in this sample than the patients in a randomized sample. Similarly, pOnpu <0 or 0i<O indicates that the access effects, which is associated with the selection of medication therapy, in this case of fluoxetine therapy, resulted in higher total costs associated with fluoxetine patients in this sample than the patients in a randomized sample. (2.C.15) E[ln(Cif)lr|n fii <A"tii ,T jni< A"i]=XifPif+0iT 1 fU A4ii+0iT 1 iu X i (2.C.16) _ ^ ( a ;)$[(i - p 2 )4/2(a; - m ;*)] yn ~ (2.C.17) 33 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The disturbance term Vjf can be derived from the difference between the actual value and the expected value of total health care costs in Equation (2.C.15) as (2.C.18) Vif =ln(Cif) - E[ln(Clf)hin fll <An m ,r|n!< AM The disturbance term Vif is heteroscedastic based on the theorem of the moments of the incidentally truncated bivariate normal distribution (Greene, 1997). To accommodate possible heteroscedasticity of disturbance terms, for example, the for fluoxetine users in Equation (2.C.18), a statistical method for correcting heteroscedasticity was developed to obtain consistent parameter estimates in Equation (2.C.15) (Viverberg, 1993; Viverberg, 1995). An adaptation specified in this study for t a two-stage antidepressant treatment management process is included in the Appendix. In addition, the logarithm transformation of health care cost/expenditure data is also a widely used method to address the heteroscedasticity. 2.C.3. Two-Stage Estimation Method for Double Lambda Method The double-lambda method was used to analyze the impact of the formulary expansion on the double selection process of the alternative treatment-drug cohorts showed in Figure 2.C.1, and to detect the double selection bias in modeling health care costs for each individual drug type. The double lambda method requires two-step estimation strategy. In the first step, a two-stage multinomial logit model was used to estimate the probability for one of the sequential treatment-drug choice cohorts based on the coefficient estimates using the statistical software Limdep version 7.0 (Greene, 1998). From the predicted probabilities from first step choice model as well as the correlation 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. coefficient p between the two-stage choices simulated by Monte Carlo algorithm, two X terms accounted for the effects of unobservable factors in the two-stage choices respectively were calculated according to Equation (2.C.16) and Equation (2.C.17). In the second step where two X terms were included as explanatory variables in an ordinary least squares (OLS) equation used to model the logarithm-transformed health care costs (log costs) for each of the treatment-drug cohorts using SAS 6.12 (SAS Institute, 1996). Including the two X terms as independent variables in the OLS model allows the bias from the unobservable variables to be explicitly modeled and, therefore, yields unbiased parameter estimates for the observed variables such as age, t gender, and race. Student t-ratios (P<0.05) calculated from parameter estimates and their standard errors were used to perform the hypothesis testing regarding the significance of individual parameters. In summary, the double-lambda method separates the treatment selection bias due to the decision of treatment initiation from the selection bias due to the decision of drug choices. Both biases might be significantly affected by the formulary expansion because of the policy impact on the process of treatment selection. As a result, the double lambda method utilizes the structural nature of the selection criteria more fully in the specification of the cost equation, and better disentangles treatment selection hbias, and allows a richer insight in the effects of treatment selection on the cost equation estimates. Note that all selection models do not control for the bias introduced by all unobservable variables - only unobservable variables in the treatment selection 35 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. process. Omitted variable bias may still occur in the cost models, if important variables that affect the health care costs are not present in the cost models. 2.D. Comparative Cost Effects across Alternative Antidepressants A commonly used approach for analyzing differences between the alternative initial antidepressants is to define a set of dummy variables in an intent-to-treat (ITT) model (Maddala, 1990). This ITT model specification estimates the “overall” comparative cost effects of the alternative antidepressants. Specifically, if the TCAs users were regarded as a reference group, it is defined that fluoxetine=l for the fluoxetine users, paroxetine=l for the paroxetine users, and etc. The impact of alternative antidepressant relative to TCAs can be estimated through a health care cost function Equation (2.C.19), which includes this set of dummy variables as extra explanatory variables and is estimated by using the treated patients only. (2.C.19) Ci=X2 (32+Rpr+e In order to understand the cost effects across the alternative antidepressants in dollar amount, the actual cost will be used in this section. In Equation (2.C.19), Q is the health care costs for the treated patients, and X2 is the explanatory variables. R denotes the set of drug dummies. To further explore the difference in the comparative cost effects of the alternative antidepressants before and after the formulary expansion, a set of variables for the interactions (i.e., policy interactions) between the drug types and the formulary expansion can be added into the ITT model, modified as (2.C.20) Ci=X2p2+Rpr+RDpr +e 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In Equation (2.C.20), the policy interaction, as defined by the product of R and D (dummy for the formulary expansion), represents change in comparative cost effect after the formulary expansion. The most challenging issue in comparing the impact across all the alternative antidepressants after the formulary expansion is to find a constant population as a standard comparison/reference group. It is a norm in antidepressant studies to set up the TCAs group as the comparative reference. However, the TCAs population might not be constant enough for the comparative reference before and after the formulary expansion because the use of TCAs was affected the substitution effects of the formulary expansion. To accommodate this dynamics in the TCAs population, the comparison group can be set as the untreated patients. Therefore the ITT model using both the policy interactions and the revised comparison group is defined as the “revised ITT model” and is expressed as (2.C.21) C=X2p2+Rpr+RDpr +£ In Equation (2.C.21), C is the health care costs for the entire depressed patients, and R is the new set of dummy variables for types of alternative drugs with the untreated patients as a comparison group, and J?D is the policy interactions as well. Now turn back to the case of existence of treatment selection bias. Studying antidepressant treatment effects is required to compare the treatment outcomes (e.g., treatment costs) across alternative therapies in a pooled sample. Neither single lambda model nor double lambda model discussed in Section 2.B or 2.C is able to make 37 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. inferences about antidepressant treatment effects because the cost regression equations in essence are subgroup analyses focusing on each drug type only. Based upon the revised ITT model, either single lambda model or double lambda model can be easily extended to the comparison of health care costs across all available antidepressants relative to no antidepressant therapy with adjustment term(s) accounted for treatment selection bias. Consequently, the revised ITT model can be added with either single or double adjustment terms accounted for treatment selection bias over the entire depressed population. The new model including both the indicator variables for types of alternative drugs and the formulary policy interactions as well as the adjustment term(s) for treatment selection bias, can be expressed as (2.C.22) C=X2p2+i?Pr+i?Dj3r +X$x +£ In Equation (2.C.22), the new term Af^is explicitly added for adjusting the effects of selection bias through either a single lambda or double lambda. As a result, this approach facilitates the analysis of comparative cost effects associated with each type of antidepressants with control for the potential treatment selection bias. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3. Formulary Policy Impact on SSRIs Use and Health Care Costs 3.A. Data and Primary Outcomes 3.A.I. Data Medi-Cal program has an established capability to deliver full-spectrum health care utilization and cost data to support research efforts. Medi-Cal covers inpatient care, outpatient care and prescription drugs for the poor and disabled. The Medi-Cal program maintains a longitudinal database as long as a recipient is eligible for the program. This database provides demographic information at the individual member level combined with institutional claims at claim level, professional service claims at service level, and prescription drug services at drug level. Data include type of services, date of services, amount billed, amount paid, and units (days) of services. Prescription drug claims identify the specific product dispensed, quantity, days supplied, and the date the prescription was filled. 3.A.2. Exclusion and Inclusion Criteria for Study Sample As the unit of analysis, treatment episodes were defined based on the dispensing date of the patient’ s initial antidepressant prescription. New treatment episodes were defined based on the patient not having filled a prescription for any antidepressant in the prior 6 months. Given this definition and the availability of data for a 5-year period, it may be possible that a single patient will experience multiple episodes of antidepressant therapy. A total of 92,438 new patient-episodes of antidepressant therapy have been constructed if patients held the following 4 conditions: 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (1) The patient’s paid claims history included at least one service with a recorded diagnosis of MDD. This restriction was designed to exclude patients who may use antidepressant medications for other therapeutic purposes. For example, TCAs may be prescribed for chronic pain or as a sleeping aid, especially in elderly patients. Fluoxetine may be prescribed for obsessive compulsive disorder. (2) More than 6 months of pre-treatment data and a minimum of one year of post-treatment data were available. This requirement was designed to focus the analysis on new treatment episodes and limited episodes’ start dates to the period after October 1,1994 and only episodes with a start date prior to early January 1998. (3) The adult patient was between 18 and 100 years of age. (4) The ambulatory patient was not institutionalized in a nursing home within 30 days from the start of therapy. New patient-episodes of treatment for MDD were excluded from this sample for the following reasons: (1) The patient's paid claims history of serious co-morbid mental disorders or indicated medication included: (a) A paid claim with a recorded diagnosis of schizophrenia, mania, bipolar depression, dementia, and chronic or transient organic psychotic conditions; 40 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (b) A prescription drug claim for a mood stabilizing medication during either the pre-treatment or post-treatment period; (c) A prescription drug claim for an antipsychotic medication prior to the treatment episode; or (d) A prescription claim for a MAO inhibitor or for two different antidepressant medications as initial therapy. A total of 22,078 episodes of care (23.9%) were excluded based on these criteria. (2) The patient’ s paid claims profile included a gap in paid claims of any type in excess of 90 days, which may indicate a temporary loss of eligibility or any other dropout from plan (47,883, 51.8%). (3) The patient consumed more than $50,000 in ambulatory cost in the 6 months prior to the treatment episode, more than $1 0 0 , 0 0 0 in total costs or 1 2 0 days of institutional services (hospital and/or nursing home care) in the 1 year post-treatment period (58 episodes, 0.1%). These restrictions trim the data for very high users of health care that is likely to be unrelated to their MDD diagnosis. (4) Patients with only paid drug claims in the post-treatment period were excluded due to the likelihood that the patient was enrolled in a Medi-Cal managed care plan that covered all services with the exception of prescription drugs (181 episodes, 0 .2 %). 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. After running the above all inclusion and exclusion criteria, the final study sample with at lease a record of MDD diagnosis in paid claim file was 6,409 patients, 5,124 (80%) of whom received antidepressant drug therapy during the treatment episode. 3.A3. Outcome Measure: Health Care Costs The patient’s monthly payment streams for various health care services, as proxy variables for health care costs, was partitioned into two periods based on the date of the initial prescription: a 6 -month prior-treatment period and a one-year post treatment period. Health care costs were also divided by types of services, including ambulatory service, hospital care, long term care, home health care, other services, and prescription drug. Any value of zero in the first post-treatment year cost was assigned as $0 . 0 1 to allow for the logarithm transformation. Health care cost/expenditure data are highly skewed and not normally distributed. A small number of large-cost observations can have a critical impact on the size of the estimated parameters and their statistical significance. Sometimes it is the high-cost patients that represent the cost-saving effect for an intervention. Logarithmically transforming health care expenditure data can reduce the influence of these large-cost observations and make traditional statistical assumptions more plausible (e.g., normality of data and homoscedasticity of the random disturbances). This concern on the skewed cost data in antidepressant study has been emphasized recently (Bemdt et al. 2000). 42 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.B. Model Specification 3.B.I. Common Variables Shared by Choice Model and Cost Model In both selection equation and cost equation, there are several common explanatory variables: (1) Patient age in decades; (2) Gender (male=l); (3) Race (black, Hispanic, and other races with white as the reference category); (4) Rural residence by county (urban counties as the reference category); (5) Count of diagnoses and prescription medications used in the 6 months prior to initiating the MDD treatment episode; (6 ) Recurrent episode of major depression; and (7) A dichotomous variable indicating the use of psychiatric services at the initiation of treatment. 3.B.2. Model Specification Test A key issue in treatment selection models is the need to carry out extensive specification tests to determine, as completely as possible, how well the models correct for both forms of treatment selection bias introduced by unobserved variables. In general, it is never possible to have full confidence that we have captured the effects of all unobserved variables associated with the treatment selection process. By extensive specification testing on the cost equation in the treatment selection model, it is possible to gain important insights into the effectiveness of the 43 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. treatment selection methods. However, testing for proper specification of treatment selection models is not different than the usual specification tests for OLS cost models. One advantage of our current study is that a carefully specified OLS cost model based on clinical and economic theory has been formulated in the previous study using 5% Medi-Cal data (McCombs et al. 1999). Consequently, keeping the model specifications very similar to that used in the McCombs et al study would be a valid approach in specifying the outcome models. Multicollinearity is the most important issue in the specification for cost model, which employs lambda term(s) calculated from the first step estimation of single-stage or two-stage choice model. As indicated above, both choice model and cost model share a set of common variables. Thus X term(s) could be close to linear relationship to explanatory variables in cost equation if all variables used in the selection model are included in the cost equation. The consequence of multicollinearity problem is loss of identifiability of the significance for X term(s) in the cost equation. The ideal solution for the multicollinearity is to theoretically or empirically find a perfect instrumental variable, which is significantly correlated with the treatment selection process (e.g., the sequential treatment-drug choice) but not correlated with the health care costs, and only applied in the choice model. The good candidate for such instrumental variable is the dummy variable for the formulary expansion. Theoretically, including fluoxetine and paroxetine in Medi- Cal drug formulary is expected significantly to change the decisions of treatment selection. However, formulary expansion is not expected to change the health care 44 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. cost directly but to change the health care costs through two forms of policy effects, the access effects and the substitution effects. It is hypothesized that both access effects and substitution effects would be controlled by the adjustment term(s), especially in the double lambda model. As a result, the formulary expansion by itself would be not a significant predictor of health care costs. In other words, the variable for the formulary expansion is a perfect instrumental variable. Empirically, the candidates for such instrumental variables unique to the choice model are the following three variables, which were tested not be statistically significant predictors of health care costs but were significant predictors of treatment selection process: (1) A dichotomous variable for community mental health center use in the prior 6 months; (2) A dichotomous variable indicating whether or not the patient was a resident of a county, where a Medi-Cal managed care initiative of prepaid health plan (PHP) was in place during the calendar year in which treatment was initiated. (3) A dichotomous variable indicating whether or not the patient was a resident of a county, where a Medi-Cal managed care initiative of county organized health systems (COHS) was in place during the calendar year in which treatment was initiated. A time trend variable, which reflected the month in which treatment was initiated (i.e., t=l for index dates in October 1994; t=40 for index dates in January 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1998), was included in cost models. The purpose of the time trend is to capture the historical effect, which is the impact of changes in the MDD population over time due to changes in exogenous factors such as economic expansion and welfare reform that evolved over time. 3.B.3. Final Model Specification The treatment-drug choice model included the explanatory variables for age, gender, race, dummy for formulary expansion, PHP, COHS, recurrent major depression, urban resident, number of concomitant drug types, number of comorbidities, and prior use of health services such as hospital use, community mental health center use (CMHC), and psychologist visit. The explanatory variables in cost model were age, squared age, gender, race, recurrent major depression, psychiatrist visit at the initiation of episode, rural resident, number of concomitant drug types, number of comorbidities, single pharmacy use, prior 6 -month costs of health services (hospital, ambulatory, drug, home health, and psychologist), and a time trend variable. In addition two X terms corresponding to the decision to seek treatment and the selection of a drug or a single X term corresponding to the single-stage selection process was also included in the cost model as well. 3.C. Results 3.C.I. Descriptive Statistics 3.C.I.I. Subjects and Changes in the Number of Patient-Episodes This study included a total of 6,409 patients with major depression diagnosis, of which only 5,124 patients (80%) initiated their antidepressant therapy with 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressants listed in Table 3.C.1 between October 1994 and January 1998. Table 3.C.1 presents the sample size for every drug group in the study sample. Almost 93.2% of all HCAs users were using trazodone, while TCAs primarily consisted of 4 different drugs: imipramine (27.2%), desipramine (15.6%), doxepin (14.8%), and nortriptyline (39.1%). Approximately 69.5% of “other new antidepressants” as initial drug, defined as the other antidepressant group, were nefazadone. When the sample was broken down into the prior- and post-formulary-expansion periods, it is informative to see the effect of the formulary expansion on the choice of treat/untreated and the choice across all available antidepressants in terms of the change in the number of patient-episodes for each treatment-cohort. The increased use of antidepressants after the formulary expansion was primarily due to a 7 fold increase in using fluoxetine (from 1 2 1 patients before the formulary expansion to 882 after the formulary expansion), and a 13 fold increase in using paroxetine (from 65 patients before the formulary expansion to 882 after the formulary expansion). Expanded antidepressant treatment using HCAs and other antidepressants, was also evident in this study sample. However, only the use of TCAs after the formulary expansion was shown to be less frequently than before, indicating possible substitution effects. This apparent increase in patients with drug therapy was not offset by a corresponding decrease in the number of MDD patients initiating a patient episode with no antidepressant therapy. The increased number of MDD patient with no antidepressant indicated that the physician were more likely to diagnose patients with MDD after gaining access to new drugs. 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE 3.C.I. Study Sample (N=6,409) by Initial Antidepressants Initial Therapy/Decision Intent to Treat Before FE After FE No Medication 1,285 486 799 Tricyclics 1,281 682 599 Imipramine 349 202 147 Amitriptyline/Perphenazine 9 8 1 Amitriptyline 16 8 8 Desipramine 200 122 78 Protriptyline 15 9 6 Doxepin 190 52 138 Trimipramine 1 0 1 Nortriptyline 501 281 220 Heterocyclics 1,308 554 754 Trazodone 1,219 535 684 Bupropion 83 13 70 Amoxapine 3 3 0 Maprotiline 3 3 0 Paroxetine 947 65 882 Sertraline 306 146 160 Fluoxetine 1,003 121 882 Other ADs 279 44 235 Venlafaxine 47 13 34 Fluvoxamine 31 12 19 Mirtazapine 7 0 7 Nefazadone 194 19 175 FE: Formulary expansion; AD: antidepressant Figure 3.C.1 demonstrates the dynamic time trend of patients who initiated their antidepressant therapy by month and by drug type. Obviously, the formulary expansion resulted in an immediate and sustained increase in the number of episodes for fluoxetine and paroxetine. Furthermore, the use of TCAs and heterocyclic 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressants did not experience an immediate offsetting decrease in new treatment episodes and the use of sertraline, an established SSRI antidepressant not added to the formulary, remained constant. It appears that any substitution of the added SSRIs for conventional antidepressants was not immediate, but may have increased over time. The sharp decline of treatment episodes for all drug types in the last few months (November of 1997 to January of 1998) is most likely attributable to the data truncation because of patient-episode construction requirement for full 1 -year post treatment data. Figure 3.C.1 Anti depressant Episode by Drug Types in the California Me (Scad Program | 90-, •a 80- W 70- 1a i% ^ td * P cP cP cP of3 ^ oP ^ A S i* x° oA a ' Calendar Month from Oct. 1994 to Jan. 1998 —#— TCA s— h— HCAs— *— Fluoxetine— * — Paroxetine— o-~ Sertraline Table 3.C.2 presents the data for overall demographics, clinical characteristics, and prior utilization with statistical comparisons for each of the drug groups relative to TCAs. The significance level was set at 0.01 to avoid possible inflated type I error. In general, all drug types were comparable along most of the characteristics listed. These 49 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. depressed patients were predominately female, white, and lived in urban area. The mean age of patients in fluoxetine group (46.2 years old) and other antidepressant group (45.0 years old) was significantly younger than the TCAs group (48.0 years old). There was a significantly lower proportion of male patients for the sertraline group (14.8%) and for the HCAs group (19.8%), as compared with the TCAs group, in which 24.0% of patients were male. There were significantly fewer urban residents (52.0%) in the other antidepressant group and significantly fewer rural residents in the sertraline group (1.6%) relative to the TCAs users. All alternative drug groups have significantly less percentage of “other” races (e.g., Asians) relative to the “other” races proportion in the TCAs patients. The use of sertraline and the other antidepressants were significantly less frequent in the African American patients than the TCAs. Clinical characteristics including the count of concomitant drugs, the count of diagnosis codes and the proportion of recurrent MDD diagnosis are comparable among all drug types including the TCAs. Finally, the data for prior 6-month health care cost by type of service only showed the limited evidence of significant cost disparity between the alternative antidepressants and the TCAs. The sertraline group used significantly more ambulatory service ($2,172) within 6 months prior to starting the medication therapy than the TCAs ($1,320). The other antidepressant group was found to use significantly less hospital service ($270) than the TCAs ($639). The paroxetine group used more home health care ($241) relative to the TCAs ($155). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE 3.C.2. Baseline Characteristics of Each Initial Antidepressant Group TCAs N=1281 Fluoxetine N=1003 Paroxetine N=947 Sertraline N=306 HCAs N=1308 Other ADs N=279 Age (years) 48.0(14.1) 46.2 (13.6)* 48.8 (15.3) 48.8 (14.9) 47.3(13.7) 45.0 (12.7)* Gender (M%) 24.0 (42.7) 20.9 (40.7) 21.8 (41.3) 14.8 (35.6)* 19.8 (39.9)* 25.2 (43.5) Urban residence (%) 66.7 (47.1) 64.6 (47.8) 63.0 (48.3) 68.6 (46.5) 64.3 (47.9) 52.0 (50.1)* Rural residence (%) 3.1 (17.4) 3.7 (18.9) 3.0 (16.9) 1.6 (12.7)* 2.8 (16.6) 5.0 (21.9) Race: Black (%) 9.2 (28.9) 6.8 (25.2) 10.5 (30.6) 3.6(18.6) 9.0 (28.7) 3.6(18.6)* : Hispanic (%) 10.0 (30.0) 11.2(31.5) 9.7 (30.6) 8.2 (27.4) 8.9(28.4) 11.1 (31.5) : Other (%) 32.0 (46.7) 21.8(41.3)* 24.3 (42.9)* 21.9 (41.4)* 25.8 (43.8)* 22.6(41.9)* PRIOR USE ($/6mon) Ambulatory 1320 (2694) 1538 (2858) 1462(2747) 2172 (4743)* 1443 (2709) 1614 (3340) Drugs 296 (701) 283 (592) 298 (566) 225 (408) 272 (568) 287 (723) Prior Hospitalization (%) 8.9 (28.5) 9.3(29.0) 11.9(32.4) 9.5 (29.3) 12.2 (32.8)* 9.0 (28.6) Hospital Costs 639 (3421) 447 (2210) 622(2519) 448 (2255) 643 (2491) 270 (1154)* Hospital Days 0.62 (3.3) 0.43 (2.1) 0.60 (2.4) 0.43 (2.2) 0.62 (2.4) 0.26(1.1)* Home Health 155 (677) 194 (769) 241 (788)* 222 (843) 166 (676) 132 (488) Other Costs 16(52) 21 (79) 19 (81) 9(30) 16 (53) 17 (74) TOTAL COSTS 2431 (4633) 2488(4127) 2646 (4063) 3084 (5446) 2549 (3958) 2328 (3728) Count of Prescriptions 0.33 (0.60) 0.32 (0.57) 0.30 (0.55) 0.37(0.61) 0.29 (0.56) 0.38 (0.66) Count of Diagnoses 3.9 (2.4) 4.0 (2.6) 4.2 (2.5) 3.6 (2.4) 4.1 (2.5) 3.8 (2.6) Recurrent MDD (%) 73.0 (44.4) 76.7 (42.3) 72.3(44.8) 78.1 (41.4) 74.1 (43.8) 78.5 (41.2) Psychiatry (%) 10.6 (30.8) 12.2 (32.7) 9.5(29.3) 7.5 (26.4) 10.2 (30.3) 10.0 (30.1) Psychologist(%) 3.6 (18.6) 4.0 (19.6) 2.4 (15.4) 5.2 (22.3) 4.3 (20.3) 3.9 (19.5) Community Mental Health Center (%) 4.2 (20.1) 5.3(22.4) 5.1 (21.9) 2.9 (16.9) 4.8 (21.4) 4.7(21.1) * Statistically significant difference in patient characteristics between patients with alternative antidepressants and patients with TCAs at pcO.Ol using Chi-square or t-tests; The standard error listed in the parentheses. 3.C.I.2. Prior Health Care Costs Before and After the Formulary Change The health care costs by type of service in the 6 months prior to starting medication treatment were characterized in Figure 3.C.2 to Figure 3.C.5. The R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. increased level of prior use of health care after the formulary change was not evenly distributed across the alternative antidepressants. Patients treated initially with TCAs, paroxetine, and sertraline exhibited statistically significant increases in the use of both ambulatory and home health care, resulting in a significant increase in total costs (+38% for TCAs; +40% for paroxetine; +100% for sertraline). Figure 3.C2. Health Care Costs in Prior-Treatment Period by Type of Service Before and After Formulary Expansion Among TCAs Users $5,000-, $4,000 $3,000- $2,000- $ 1,000- $ 0- *** 1673 1009 | _ ■ I 343 243 587 697 103 212 Hospital Cost Home Health Care Cost Total Costs Ambulatory Cost Drug Cost ■ Before Formulary Expans ionH After Formulary Expans bn Figure 3.C3 . Health Care Costs in Prior-Treatment Period by Type of Service Before and After Formulary Expansion Among Paroxetine Users $5,000-, $4,000 , 2699 $3,000 1504 SOS $2,000 $1,000- 295 298 635 621 82 252 Total Costs Ambulatory Cost Drug Cost Hospital Cost Home Health Care Cost ■ Before Formulary ExpansionB After Formulary Expansion 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 3.C.4. Health Care Costs in Prior-Treatment Period by Type of Service Before and After Formulary Expansion Among Sertraline Users $5,000- $4,000- $3,000- $ 2,000- $ 1,000- $ 0- 2982 251 201 Total Costs Ambulatory Cost Drug Cost Hospital Cost Home Health Care Cost Before Formulary Expansions After Formulary Expansion In contrast, fluoxetine exhibited the highest average total prior use in the pre formulary expansion period, but fell behind both TCAs and paroxetine in the post expansion period. While prior use did increase slightly for fluoxetine patients in the post-expansion period (+15% overall), the majority of this cost increase was due to a five-fold increase in home health cost. Combined with the sample size data shown in Table 3.C.1, these data suggest that in the post-expansion period, the patients who initiated antidepressant therapy with fluoxetine were less severely ill than the patients prescribed paroxetine. 53 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 3.C.5. Health Care Costs in Prior-Treatment Period by Type of Service Before and After Formulary Expansion Among Fluoxetine Use is $5,000, $4,000- 3.C.2.I. Factors Influencing Two-Stage Treatment-Drug Choice The impact of model parameters (patient characteristics, prior utilization, and formulary expansion in particular) on the decision to seek treatment and the choice across the alternative drugs was estimated via a two-stage sequential treatment-drug choice model. The parameter estimates for the sequential treatment-drug choice model are reported in Table 3.C.3 along with the corresponding odds ratio for parameter estimates listed beneath. The parameter estimates listed in each of the first 5 columns (j3rii or prdu) represent the effects of model parameters on the choice across the alternative antidepressants relative to TCAs. The parameter estimates listed in the last column (Pi or Pid) represent the effects of model parameters on the decision to seek treatment for TCAs population relative to the untreated patients. As a result, the effects of model parameters on the decision to seek treatment for a particular Total Costs Ambulatory Cost Drug Cost Hospital Cost Home Health Care Cost I 3.C.2. Double Lambda Method versus Single Lambda Method 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. antidepressant other than TCAs relative to the untreated patients can be measured as the summation of parameter estimates (Prii+Pi or prdii+Pid)- In terms of the odds ratio, these effects can be measured as the product of odds ratio for TCAs and odds ratio for a specific antidepressant. In particular for the formulary expansion, the estimated effect of the formulary expansion on the decision to seek treatment was the access effects associated with the formulary expansion and the estimated effect of the formulary expansion on the drug choice was the substitution effects. In general, adding fluoxetine and paroxetine in the Medi-Cal formulary had a global, yet unevenly distributed substitution effects on the choice across the alternative drugs relative to TCAs. A significant increase in the likelihood that a patient receives fluoxetine (odds ratio=9.44, pcO.OOl), or paroxetine (odds ratio=17.8, pcO.OOl) relative to TCAs was the evidence of the substitution effects on the use of these two added SSRls after the formulary expansion. The effect on the slightly increased likelihood of receiving HCAs (odds ratio=1.59, pcO.OOl) relative to TCAs might also be due to either the observed reduction in prescriptions of TCAs or the substitution of HCAs for TCAs after the formulary expansion. As expected, the other new antidepressants recently approved by FDA are likely to be prescribed in the post- formulary-expansion period in terms of significantly higher odds on receiving other antidepressants (odds ratio=6.82, pcO.OOl) after the formulary expansion, which is hard to be attributed to the formulary expansion. However, no correspondingly significant increase in the likelihood of patient-episodes receiving sertraline relative to the TCAs was found in this study sample (odds ratio=1.21, p=0.1556). Therefore, the 55 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. results measuring the substitution effects of the formulary expansion based on the two- stage multinomial logit model conform to the changes in sample size before and after the formulary change in Table 3.C.I. Relative to the untreated patients, the access effects associated with the formulary expansion can be also studied based on the two-stage multinomial logit model as well. The last column of Table 3.C.3 was the estimated impact of determinants for choosing TCAs relative to the untreated population. The formulary expansion was shown to reduce the likelihood of using the TCAs relative to the untreated population (odds ratio=0.59, pcO.OOl). The additional data can be more 'deeply explored for the access effects of the formulary expansion for a specific antidepressant by multiplying the odds ratio of the formulary expansion for TCAs with the odds ratio of the formulary expansion for the antidepressant. In other words, this calculated product of odds ratios roughly measured the access effects associated with formulary expansion for the antidepressants. The highly increased likelihood for either fluoxetine (odds ratio=9.4*0.59=5.6), or paroxetine (odds ratio=17.8*0.59=10.4) was found to show better access to these two added SSRIs. HCAs and sertraline might be not associated with the access effects of the formulary expansion. Relative to the untreated patient population, MDD patients in the Medi- Cal program did not change much in the likelihood to use sertraline as initial drug (odds ratio=1.21 *0.59=0.71) after the formulary expansion. In the same way, it was found that relative to this untreated population, MDD patients were almost at the same 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. likelihood of using HCAs (odds ratio=1.59*0.59=0.94) after the formulary expansion as before. TABLE 3.C.3. The Coefficient Estimates and Their Corresponding Odds Ratio of Treatment- Brtig Choice Model Estimated by Two-Stage Multinomial Logit Method__________________ Variable Antidepressant Choice (reference group: TCAs) Treat (Y/N) Fluoxetine Paroxetine Sertraline HCAs Other ADs Age -0.135*** -0.013 0.071 -0.034 -0.190*** 0.119*** 0.87 0.99 1.07 0.97 0.83 1.13 Gender (M=l) -0.250* -0.311** -0.571** -0.273** -0.005 -0.130 0.78 0.73 0.56 0.76 1.00 0.88 Formulary 2.245*** » 2.879*** 0.194 0.465*** 1.919*** -0.526*** 9.44 17.80 1.21 1.59 6.81 0.59 PHP -0.099 -0.141 -0.200 0.014 -0.418** -0.451*** 0.91 0.87 0.82 1.01 0.66 0.64 COHS -0.321 -0.465 1.502*** 0.160 -0.304 -0.512* 0.73 0.63 4.49 1.17 0.74 0.60 Black -0.586*** -0.040 -1.023** -0.207 -1.359*** -0.203 0.56 0.96 0.36 0.81 0.26 0.82 Hispanic -0.068 -0.108 -0.309 -0.257 -0.074 0.245 0.93 0.90 0.73 0.77 0.93 1.28 Other race -0.561*** -0.437*** -0.509** -0.339*** -0.449** 0.340*** 0.57 0.65 0.60 0.71 0.64 1.40 Rural Resident 0.226 0.089 -0.448 0.151 0.415 0.113 1.25 1.09 0.64 1.16 1.51 1.12 Specialist 0.250 -0.005 -0.390 -0.023 0.048 1.462*** 1.28 1.00 0.68 0.98 1.05 4.31 Recur. MDD 0.190 -0.064 0.298 0.050 0.252 -0.019 1.21 0.94 1.35 1.05 1.29 0.98 # o f diagnosis 0.051** 0.088*** -0.030 0.046** 0.027 0.036* 1.05 1.09 0.97 1.05 1.03 1.04 # o f Rx 0.064 -0.051 0.113 -0.147* 0.266* -0.078 1.07 0.95 1.12 0.86 1.30 0.92 Prior Hosp 0.460*** 1.58 Prior Psych 0.312 1.37 Prior CMHC -0.815*** 0.44 For each variable, the odds ratio (in italic) for coefficient estimate is listed beneath. * p<0.05 ** p<0.01 *** pcO.OOl Gender: male=l and female=0; PHP: prepaid health plan; COHS: county organized health system; Recur. MDD: recurrent MDD diagnosis; Prior Hosp: prior hospitalization; Prior Psych: prior psychologist visit; Prior CMHC: prior community mental health center use. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In summary, the results for TCAs and two added SSRIs jointly demonstrated that there was a significant substitution of added SSRIs for TCAs and that MDD patients had a better access to the 2 added SSRIs after the formulary expansion. Other drug types were not found to be associated with the access effects although there was some evidence of the substitution effects for both HCAs and other new antidepressants. 1 Several patient characteristics also affect the decision to seek treatment and the drug choice. Relative to TCAs users, the elderly patients tended to less likely to use fluoxetine (odds ratio=0.873, p<0.001) and other antidepressants (odds ratio=0.967, pcO.OOl). However, elderly patients tended to more likely to use TCAs relative to the untreated population (odds ratio=1.13, pcO.OOl). Interestingly, being a male or being a minority (i.e. African American, Hispanic, and other minorities) were less likely to receive the SSRI antidepressants, especially fluoxetine. Being hospitalized prior to initiation of new MDD episode was more likely to seek medication treatment (odds ratio=1.58, pcO.OOl). On the contrary, if having used the community mental health center, MDD patients tended to less likely to seek medication treatment (odds ratio=0.44, pcO.OOl). The managed care initiatives, PHP or COHS, removed patients who were more likely to use antidepressant from the fee-for-service population (odds ratio=0.63, pcO.OOl for PHP; odds ratio=0.60, pcO.OOl for COHS). Only COHS was found to increase the use of sertraline relative to TCAs (odds ratio=4.49, pcO.OOl). As compared with TCAs, the number of comorbidities were positive correlated with the use of antidepressants: fluoxetine (odds ratio=1.05, pcO.Ol), paroxetine (odds 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ratio=1.09, pcO.OOl) while the number of comorbidities were also correlated with the use of TCAs as compared to untreated population (odds ratio=1.04, p<0.05). However, there was no consistent pattern in the relationship between the number of concomitant drugs used in prior period and choice of antidepressants. 3.C.2.2. Calculate Treatment Selection Correction Terms The model parameter estimates from the above two-stage treatment-drug choice model were then utilized to calculate both the single lambda term and double lambda terms. The key element for calculating the lambda term(s) is the probability for each endpoint in the choice processes described in section 2.B and in section 2.C. Table 3.C.4A presents the actual probabilities and the estimated probabilities associated with each alternative antidepressant before and after the formulary change. Accordingly, the actual probability and estimated probability of untreated patients can be easily calculated from the Table 3.C.4A (not reported here). The small difference between actual and predicated probabilities across all alternatives demonstrated the good prediction power of the two-stage treatment-drug choice model, and also demonstrated significant dependence on the impact of the formulary expansion. TABLE 3.C.4A. Actual and Predicated Probability for Each Alternative Antidepressant Group Before and After the Formulary Change______________ ________________________________ Predicated Probability Actual Probability Drug Type Before After Before After Fluoxetine 6.1% 21.8% 5.8% 20.5% Paroxetine 3.1% 21.7% 3.1% 20.5% Sertraline 10.9% 6.5% 7.0% 3.7% HCAs 27.2% 18.0% 26.4% 17.5% Other ADs 2.7% 6.3% 2.1% 5.5% TCAs 22.5% 18.6% 32.5% 13.9% 59 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The difference between the double lambda method and the single lambda method is that a unique element, the correction coefficient between the two-stage choice process is required for calculating the double lambda. The correction coefficient carries the information on the interdependence between the access effects and substitution effects through the two-stage choice process. Table 3.C.4B presents the correlation coefficients between the sequential decisions to seek treatment and to choose a particular drug before and after the formulary expansion. Before the formulary expansion, the correlation between the decision to seek treatment and the drug choice is only positive in the patients prescribed TCAs (0.29±0.11). This result indicated that the depressed patients, if treated, were most likely to use TCAs. Within the HCAs users, there was a very small negative association between the decision to seek treatment and the drug choice before formulary expansion (-0.07 ±0.09). All other drug types demonstrated a negative association between these two-stage choices: fluoxetine (-0.46±0.10), paroxetine (-0.52±0.06), sertraline (-0.48dh0.17), and other antidepressant (-0.5610.07). These results reflected the restriction of prior authorization requirements on these SSRIs or other new drugs prior to the formulary expansion. After the formulary expansion, the TCAs users had a dramatic change from the positive value before formulary expansion to a negative value (-0.3110.11) of correlation coefficient, indicating the effects of substitution of alternative medication for TCAs. Compared with TCAs, an opposite direction of change to less negative correlation coefficients was found in the fluoxetine users (-0.2010.09) and the 60 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. paroxetine users (-0.19 ±0.10) after the formulary change. The correlation coefficients for either fluoxetine or paroxetine did not reach the positive territory because there was a concurrent increase number of untreated patients with MDD diagnosis, which ends up with a negative coefficient to offset the influence from the new-entry of untreated patients after the formulary expansion. It seems that the calculated double lambda terms could account for increased likelihood to diagnose patient with MDD. There was almost no change of correlation coefficient in the sertraline users (- 0.49±0.15). All these changes in correlation coefficients reflected the changes in sample size showed in Table 3.C.I. TABLE 3.C.4B. Correlation of Coefficients between the Decision to Seek Treatment and the Alternative Drug Choice Before and after the Formulary Expansion_________________________ Drug Type Before FE After FE Mean Std Mean Std Fluoxetine -0.46 0.010 -0.20 0.094 Paroxetine -0.52 0.063 -0.19 0.10 Sertraline -0.48 0.17 -0.49 0.15 HCAs -0.072 0.093 -0.26 0.095 Other ADs -0.56 0.072 -0.49 0.084 TCAs 0.29 0.11 -0.31 0.11 Std: standard deviation. FE: formulary expansion of fluoxetine and paroxetine 3.C.2.3. Treatment Selection-Corrected Log Total Costs Models 3.C.2.3.1. Impact of Treatment Selection Bias on Total Health Care Costs A critical element in the attempt to correct the log total cost estimates for treatment selection bias is to identify the included treatment selection terms (i.e., double lambda terms). Identifiability is enhanced, or equivalently, multicollinearity in the equation is reduced, if the treatment selection terms contain the information different from the variables already present in the log total costs equation. Obviously, a special consideration was given to replace the set of dummy variables indicating 61 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. prior uses of health care facilities with the corresponding variables for prior 6-month costs of ambulatory care, hospital care, drug, home healthcare, and psychologist visit. More importantly, as indicated in section 3.B, four unique variables (formulary expansion, PHP, COHS, and CMHC use) in the treatment-drug choice model were excluded from total costs model to ensure a better model specification. The double lambda method separated the selection bias into two forms: the bias due to the decision to seek treatment (treatment initiation or access effects bias) and the bias due to the choice across the alternative drugs (drug choice or substitution effects bias). A negative sign of each IMR coefficient in a subgroup/drug class regression means that actual sample of patients treated with this drug or drug class would have used more health care services than a hypothetical sample randomly drawn from the patients with MDD diagnosis. Conversely, the positive sign demonstrates that the actual sample would have lower costs than a random sample of MDD patients. Without adjustment for the bias due to either treatment initiation or drug choice would introduce bias into the estimated effects of patient characteristics such as age, gender, and race. The improvements on parameter estimates can only be observed in the subgroup regression model for each individual antidepressant. The benefit of bias adjustment on other parameter estimates in regression will be presented in the following Section 3.C.2.3.2. The results of double treatment selection-corrected log total costs model for each antidepressant are presented in Table 3.C.5A to Table 3.C.5F, where the coefficients for the selection bias adjustment terms were provided. The OLS log total 62 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. costs model and two single treatment selection-corrected log total costs models with IMR estimated from different study sample (treated only patients versus entire population) are also listed as the comparison models. When compared to the single lambda method estimated using entire MDD patient population, the double lambda method separates the overall treatment selection bias into double selection bias. In addition, as opposed to the standard single lambda method estimated using treated only patients, the double lambda method can answer the question of whether or not it is possible to remove the influence of treatment initiation bias simply by excluding the untreated patients from the analysis. TCAs Patients: As a comparison group in the study reported in Table 3.C.5A, the TCAs- treated patients were found to have the significantly negative drug choice bias by all three different treatment selection bias models. In the double lambda model, while the treatment initiation bias (0.253, p=0.4886) was not significant, the drug choice was associated with the negative selection bias (-0.620, p=0.0042). These results were consistent with the significant substitution effects on the use of TCAs after the formulary expansion as showed in Table 3.C.3. The negative sign for drug choice bias also suggested that the process of substituting SSRIs for TCAs resulted in an increase in total costs associated with the TCAs used as the initial drug in this sample relative to what would be found in an randomly selected TCAs sample. The different samples estimated by single lambda method were also found to have the significant negative treatment selection bias (-0.557, p=0.0059 if adjusted for 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. whole population; -0.604, p=0.0006 if adjusted for only treated patients). The negative sign for overall treatment selection bias suggested that the aggregate effect of the formulary expansion resulted in an increase in total costs associated with the patients who used the TCAs as their initial drug relative to what would be found in an randomly selected MDD sample. TABLE 3.C.5A. Estimates of Log Total Costs Equation for the TCAs Patient Episodes (N=l,281) Variable OLS (Adj, R2 =0. 3514) Single X (Treated Patients) (Adj, R 2=0.357Q) Single X (Whole Sample) (Adj, R 2=0.3548) Double X (Whole Sample) (Adj, R2 =0.3549) E stim ate P-value Estimate P-value Estimate P-value Estimate P-value Age -0.224 0.0389 -0.201 0.0636 -0.202 0.0618 -0.204 0.0593 Agesq 0.026 0.0113 0.025 0.0149 0.026 0.0133 0.025 0.0178 Gender 0.059 0.3369 0.127 0.0474 0.087 0.1586 0.145 0,0397 Black 0.064 0.4879 0.154 0.1056 0.096 0.2989 0.172 0.0955 Hispanic -0.022 0.8050 0.025 0.7814 0.029 0.7533 -0.002 0.9841 Other race -0.223 0.0002 -0.111 0.1004 -0.126 0.0678 -0.147 0.0310 Rural Resident -0.368 0.0961 -0.427 0.0532 -0.386 0.0803 -0.441 0.0487 Specialist -0.130 0.1151 -0.126 0.1233 -0.061 0.4791 -0.201 0.0880 Recurrent MDD 0.178 0.0020 0.150 0.0099 0.156 0.0072 0.155 0.0079 # of Concomitant Rx 0.059 0.1717 0.067 0.1205 0.058 0.1811 0.076 0.0856 # of Diagnoses 0.056 0.0000 0.043 0.0004 0.048 0.0001 0.042 0.0007 Single Pharmacy Use -0.136 0.2685 -0.117 0.3401 -0.123 0.3153 -0.114 0.3537 Prior Cost (in $1,000) Hospital 0.071 0.0000 0.070 0.0001 0.072 0.0001 0.069 0.0000 Ambulatory 0.150 0.0000 0.149 0.0001 0.148 0.0001 0.149 0.0000 Drag 0.205 0.0000 0.206 0.0001 0.206 0.0001 0.206 0.0000 Home Health 0.236 0.0000 0.245 0.0001 0.243 0.0001 0.244 0.0000 Psychologist 0.503 0.4569 0.535 0.4263 0.592 0.3802 0.452 0.5043 Time Trend 0.015 0.0000 0.003 0.5387 0.005 0.2239 0.006 0.1687 X .j for treated (y/n) 0.253 0.4886 X - u j t /j for drug choice T .2 • . . 1 !_j - _ J »_____ .... -0.604 0.0006 -0.557 0.0059 -0.620 0.0042 R is adjusted for number of independent variables Fluoxetine Patients: For the fluoxetine recipients in Table 3.C.5B, the most important result is that the selection bias resulted from the process of treatment initiation was statistically 64 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. significant and negative (-0.662, p=0.0401), while the drug choice bias was not statistically significant and positive (0.104, p=0.7372). The result of negative treatment initiation bias indicated that these fluoxetine users were higher health care users as compared to a randomly selected sample. Significant treatment initiation bias could be caused by the significant access effects on the use of fluoxetine after the formulary expansion, which can change the unobservable characteristics in the fluoxetine-treated patients. In contrast, if all MDD-diagnosed patients including the untreated depressed patient were used in the selection rule of a single-stage selection, the single selection bias across all choice options was not significant and negative (-0.123, p=0.4511). The sign and value range of drug choice bias support the conjecture that the treatment selection bias estimated by the single lambda term is a mixture of two forms of treatment selection bias corresponding to the decision to seek treatment and the choice of alternative drugs, if treated. As compared to the double lambda method, lack of the ability to identify treatment initiation bias demonstrated a methodological drawback due to absence of statistical vehicles to capture the two forms of treatment selection effects separately in such a single lambda method. Simply expanding study population did not help researchers to identify the significant access effects associated with the formulary expansion. Furthermore, if the selection process for drug choice was considered only within the treated population as indicated in Figure 2.B.1, the result for the single treatment selection-corrected model showed a negative single selection bias (-0.056, 65 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. p=0.7462). It suggested that simply excluding the untreated patients from the study sample did not fully remove the influence of the access effects. It also implied that it need be cautious to the underlying assumption of constant treated population before and after the formulary expansion when as usual a comparative ITT model incorporated with single lambda adjustment would be conducted by only using the treated patients. As a result, the ITT models in this MDD study will only be conducted in the whole sample including MDD patients with no antidepressant therapy. TABLE 3.C.5B. Estimates of Log Total Costs Equation for the Fluoxetine Users (N=l,003) Variable OLS Single X Single X Double X (Adj, R2 =0.3406) (Treated Patients) (Whole Sample) (Whole Sample) (Adj, R2 =0.3399) (Adj, R2 =0.3403) (Adj, Rz =0.3421) Estimate P-value Estimate P-value Estimate P-value Estimate P-value Age -0.156 0.1133 -0.160 0.1073 -0.165 0.0969 -0.172 0.0821 Agesq 0.019 0.0476 0.019 0.0463 0.020 0.0435 0.021 0.0323 Gender 0.027 0.6648 0.027 0.6606 0.023 0.7151 -0.022 0.7458 Black 0.033 0.7425 0.024 0.8172 0.007 0.9454 -0.058 0.6018 Hispanic -0.169 0.0404 -0.164 0.0484 -0.158 0.0589 -0.139 0.0976 O ther race -0.019 0.7700 -0.025 0.7104 -0.031 0.6349 -0.031 0.6390 Rural Resident 0.079 0.6646 0.083 0.6490 0.094 0.6064 0.156 0.4003 Specialist -0.088 0.2617 -0.081 0.3260 -0.061 0.4793 0.052 0.6222 Recurrent MDD 0.112 0.0649 0.115 0.0611 0.119 0.0525 0.123 0.0466 # of Concomitant Rx 0.065 0.1600 0.068 0.1498 0.070 0.1339 0.060 0.2014 # of Diagno ses 0.025 0.0200 0.025 0.0190 0.027 0.0146 0.035 0.0029 Single Pharmacy Use -0.302 0.0044 -0.302 0.0044 -0.304 0.0042 -0.318 0.0028 Prior Cost (in $1,000) Hospital 0.051 0.0000 0.051 0.0001 0.051 0.0001 0.055 0.0000 Ambulatory 0.140 0.0000 0.139 0.0001 0.139 0.0001 0.138 0.0000 Drag 0.253 0.0000 0.252 0.0001 0.252 0.0001 0.250 0.0000 Home Health 0.195 0.0000 0.194 0.0001 0.193 0.0001 0.195 0.0000 Psychologist 0.351 0.6854 0.363 0.6755 0.394 0.6501 0.548 0.5295 Time Trend 0.011 0.0001 0.012 0.0042 0.013 0.0012 0.013 0.0000 X t for treated (y/n) -0.662 0.0401 X rx/ i for drug choice -0.056 0.7462 -0.123 0.4511 0.104 0.7372 5? is adjusted for number of independent variables 66 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Paroxetine Patients: Table 3.C.5C demonstrates that the double lambda method was not able to detect any significant selection bias among paroxetine group. In the double lambda method, the treatment initiation bias is positive and not significant (0.347, p=0.3279) and the drug choice bias is also positive and not significant (0.116, p=0.7296). As expected, following the conjecture of mixture of two forms of treatment selection bias, it was found that the direction for coefficient of single lambda term by using whole sample is positive (0.300, p=0.0517). The similar coefficient estimated only using the treated population is also positive and statistically significant (0.315, p=0.0442), indicating an overall treatment selection bias. These results suggested that paroxetine used as the initial drug was not consistent with the pattern of fluoxetine used as the initial drug, especially in the aspect of unobservable characteristics. After the formulary expansion, the MDD patients had better access to both fluoxetine and paroxetine at the same time. However, the formulary expansion had different effects on fluoxetine and paroxetine. The improved access to two SSRI antidepressants could alter the use of antidepressant drug therapy in intended and unexpected fashion. The data for health care utilization or clinical characteristics prior to the episode might provide some indirect and limited evidence to distinguish the two components of the access effects. These data suggest that in the post-expansion period, the patients who initiated antidepressant therapy with fluoxetine were less severely ill (unexpected access effects) than the patients prescribed paroxetine. 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE 3.C.5C. Estimates of Log Total Costs Equation for the Paroxetine Users ^=947^ __ Variable OLS Single X Single X Double X (Adj, R2 =0.3609) (Treated (Whole Sample) (Whole Sample) Patients) (Adj, R2 =0.3628) (Adj, R2 =0.3604) (Adj, R2 =0.3630) E stim ate P-value E stim ate P -value E stim ate P -value E stim ate P -value Age -0.101 0.2979 -0.094 0.3312 -0.091 0.3438 -0.096 0.3208 Agesq 0.015 0.1084 0.013 0.1460 0.013 0.1549 0.014 0.1354 Gender 0.096 0.1490 0.111 0.0959 0.121 0.0723 0.125 0.0857 Black 0.070 0.4247 0.014 0.8757 0.039 0.6594 0.083 0.4373 Hispanic 0.008 0.9278 0.006 0.9468 0.004 0.9625 0.002 0.9854 Other race 0.024 0.7087 0.027 0.6794 0.027 0.6765 0.029 0.6495 Rural Resident -0.153 0.4578 -0.163 0.4288 -0.178 0.3886 -0.190 0.3681 Specialist -0.007 0.9350 0.004 0.9650 -0.021 0.8194 -0.056 0.6163 Recurrent MDD 0.105 0.0719 0.135 0.0252 0.133 0.0272 0.122 0.0491 # of Concomitant Rx 0.018 0.7141 0.029 0.5652 0.030 0.5509 0.022 0.6617 # of Diagnoses 0.049 0.0000 0.039 0.0020 0.037 0.0035 0.040 0.0028 Single Pharmacy Use -0.315 0.0031 -0.300 0.0048 -0.299 0.0049 -0.307 0.0040 Prior Cost (in $1,000) Hospital 0.065 0.0000 0.066 Q .O O O l 0.065 0.0001 0.064 0.0000 Ambulatory 0.135 0.0000 0.136 0.0001 0.136 0.0001 0.135 0.0000 Drug 0.318 0.0000 0.312 0.0001 0.312 0.0001 0.316 0.0000 Home Health 0.262 0.0000 0.271 0.0001 0.270 0.0001 0.263 0.0000 Psychologist 1.127 0.1341 1.152 0.1251 1.141 0.1288 1.105 0.1424 Time Trend 0.010 0.0019 0.004 0.3777 0.004 0.3229 0.009 0.0081 for treated (y/n) 0.347 0.3279 X .r x /1 for drug choice 0.315 0.0442 0.300 0.0517 0.116 0.7296 R is adjusted for number of independent variables Sertraline Patients: Interestingly, in the sertraline-treated patients, the dual treatment selection- corrected regression in Table 3.C.5D indicated that there was neither the significant treatment initiation bias (-1.442, p=0.0523) nor the significant bias due to drug choice (-0.023, p=0.9418). If the single lambda method was used in the whole depressed population, there was a negative but not significant selection bias in the single-stage choice process (-0.236, p=0.1758), as was there if the single lambda method was used in the treated patients (-0.219, p=0.1871). These results suggested that sertraline, as 68 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. an SSRI antidepressant not included in the Medi-Cal formulary, was quite neutral to either the access effects or the substitution effects associated with the formulary change involved with fluoxetine and paroxetine. TABLE 3.C.5D. Estimates of Log Total Costs Equation for Sertraline Users (N=306) ___ Variable OLS Single k Single £ Double £ (Adj, R2 =0.4196) (Treated Patients) (Whole Sample) (Whole Sample) (Adj, R2 =0.4212) (Adj, R2 =0.4214) (Adj, R2 =0.4248) E stim ate P -value E stim ate P -value E stim ate P-value E stim ate P -value Age -0.175 0.3348 -0.151 0.4070 -0.150 0.4101 -0.176 0.3303 Agesq 0.025 0.1322 0.023 0.1593 0.023 0.1584 0.026 0.1185 Gender 0.252 0.0591 0.203 0.1426 0.192 0.1693 0.242 0.0963 Black -0.384 0.1183 -0.498 0.0560 -0.514 0.0515 -0.244 0.3856 Hispanic 0.165 0.3273 0.122 0.4780 0.122 0.4753 0.142 0.4004 Other race 0.085 0.4543 0.026 0.8289 0.024 0.8421 0.024 0.8338 R ural Resident 0.360 0.4342 0.31? 0.4942 0.322 0.4837 0.344 0.4532 Specialist -0.215 0.2356 -0.263 0.1539 -0.250 0.1715 -0.187 0.3844 Recurrent MDD 0.039 0.7256 0.044 0.6946 0.045 0.6837 0.048 0.6687 # of Concomitant Rx 0.077 0.3350 0.093 0.2475 0.091 0.2564 0.071 0.3726 # of Diagnoses 0.044 0.0452 0.032 0.1783 0.033 0.163 0.039 0.0849 Single Pharmacy Use 0.268 0.2084 0.283 0.1847 0.279 0.1898 0.219 0.3052 Prior Cost (in $1,000) Hospital 0.001 0.9596 0.008 0.7126 0.009 0.6825 0.013 0.5556 Ambulatory 0.120 0.0000 0.120 0.0001 0.120 0.0001 0.123 0.0000 Drug 0.456 0.0005 0.461 0.0004 0.462 0.0004 0.457 0.0005 Home Health 0.144 0.0182 0.154 0.0122 0.154 0.012 0.149 0.0141 Psychologist -1.700 0.2530 -1.843 0.2160 -1.808 0.224 -1.698 0.2563 Time Trend 0.012 0.0025 0.009 0.0411 0.010 0.0352 0.012 0.0037 X i for treated (y/n) -1.442 0.0523 X ikn for drug choice -0.219 0.1871 -0.236 0.1758 -0.023 0.9418 R is adjusted for number of independent variables HCAs Patients: In Table 3.C.5E, the results of the double lambda method for the HCAs users demonstrated the significant drug choice bias (-0.737, p=0.0227), while there was no evidence of the significant treatment initiation bias (0.012, p=0.9720). Similarly, it was found that there was a significant single selection bias using the single lambda 69 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. method in either the whole sample (-0.667, p=0.0364) or in the treated patients (- 0.721, p=0.0092). These results similar to TCAs might be attributable to the observed trend of shifting the HCAs patients to the added SSRIs after the formulary expansion. TABLE 3.C.5E. Estimates of Log Total Costs Equation for the HCAs Users (N=l,308) _ _ _ Variable OLS Single X Singled Double X (Adj, R2 =0.3299) (Treated Patients) (Whole Sample) (Whole Sample) (Adj, R2 =0.3329) (Adj, R2 =0.3317) (Adj, R2 =0.3318) E stim ate P -value E stim ate P -value E stim ate P -value E stim ate P -value Age -0.278 0.0099 -0.264 0.0141 -0.266 0:0137 -0.273' 0.0111 Agesq 0.033 0.0017 0.032 0.0027 0.033 0.0021 0.032 0.0023 Gender -0.075 0.2213 -0.111 0.0783 -0.136 0.0451 -0.088 0.2195 Black 0.229 0.0084 0.258 0.0031 0.207 0.0178 0.263 0.0063 Hispanic -0.202 0.0193 -0.237 0.0068 -0.227 0.0093 -0.229 0.0087 Other race -0.153 0.0088 -0.159 0.0064 -0.158 0.0066 -0.158 0.0067 Rural Resident -0.056 0.7673, -0.053 0.7779 -0.012 0.9506 -0.061 0.7527 Specialist -0.002 0.9836 -0.010 0.9042 0.060 0.4795 -0.032 0.7704 Recurrent MDD 0.149 0.0073 0.143 0.0102 0.146 0.0088 0.143 0.0101 # of Concomitant Rx 0.035 0.4488 -0.022 0.6604 -0.021 0.6942 -0.006 0.9056 # of Diagnoses 0.025 0.0225 0.029 0.0075 0.033 0.0042 0.027 0.0278 Single Pharmacy Use -0.396 0.0005 -0.381 0.0008 -0.390 0.0006 -0.381 0.0008 Prior Cost (in $1,000) Hospital 0.063 0.0000 0.063 0.0001 0.066 0.0001 0.062 0.0000 Ambulatory 0.145 0.0000 0.145 0.0001 0.145 0.0001 0.145 0.0000 Drag 0.317 0.0000 0.317 0.0001 0.318 0.0001 0.317 0.0000 Home Health 0.219 0.0000 0.230 0.0001 0.225 0.0001 0.229 0.0000 Psychologist -0.373 0.4426 -0.369 0.4469 -0.303 0.5329 -0.391 0.4246 Time Trend 0.018 0.0000 0.010 0.0038 0.013 0.0002 0.012 0.0004 X ! for treated (y/n) 0.012 0.9720 A - r x /i for drug choice -0.721 0.0092 -0.667 0.0364 -0.737 0.0227 R is adjusted for number of independent variables Other antidepressants Patients: The results for the other antidepressant patients in Table 3.C.5F are very similar to those for the sertraline users. The dual treatment selection-corrected regression found neither the significant treatment initiation bias (-1.275, p=0.1250) 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. nor the significant bias due to drug choice (-0.052, p=0.8769). Neither the whole depressed population nor the treated patients estimated by single lambda methods was found to have the treatment selection bias in treatment choice process (-0.021 p=0.9608 vs -0.020 p=0.9659 for the respective samples). Lack of the impact of treatment selection bias on total health care costs can be interpreted as either relatively small sample size or the implicit criteria for choosing newly approved antidepressants. These criteria might not be reflected in the two-stage multinomial choice model because the increased use of the other new antidepressant would not be appropriately characterized as the effects of the formulary expansion. TABLE 3.C.5F. Estimates of Log* Total Costs Equation for the Other AD Users (N=279) Variable OLS Single X Single X Double X (Adj, R2 =0.2837) (Treated Patients) (Whole Sample) (Whole Sample) (Adj, R2 =0.2808) (Adj, R2 =0.2808) (Adj, R2 =0.2855) Estimate P-value Estimate P-value Estimate P-value Estimate P-value Age 0.088 0.6531 0.087 0.6607 0.087 0.6599 0.073 0.7110 Agesq -0.002 0.9016 -0.002 0.9010 -0.002 0.9012 -0.001 0.9404 Gender 0.250 0.0337 0.252 0.0514 0.252 0.0402 0.231 0.0568 B lack 0.256 0.3782 0.248 0.4834 0.247 0.4808 0.406 0.2313 Hispanic 0.036 0.8187 0.036 0.8176 0.036 0.817 0.038 0.8071 Other race -0.001 0.9963 -0.002 0.9866 -0.002 0.9853 -0.010 0.9352 Rural Resident -0.860 0.0036 -0.855 0.0070 -0.854 0.0071 -0.749 0.0171 Specialist -0.141 0.3934 -0.142 0.3938 -0.140 0.4012 -0.060 0.7848 Recurrent MDD 0.122 0.3000 0.124 0.3160 0.124 0.3124 0.114 0.3387 # of Concomitant Rx 0.119 0.1196 0.121 0.1967 0.121 0.168 0.123 0.1075 # of Diagnoses 0.046 0.0240 0.046 0.0245 0.046 0.0244 0.052 0.0210 Single Pharmacy Use -0.093 0.6227 -0.093 0.6230 -0.093 0.6228 -0.094 0.6182 Hospital 0.104 0.0139 0.104 0.0143 0.104 0.0141 0.107 0.0127 Ambulatory 0.101 0.0000 0.101 0.0001 0.101 0.0001 0.101 0.0000 Drag 0.136 0.0553 0.135 0.0568 0.135 0.0566 0.140 0.0480 Home Health 0.261 0.0231 0.261 0.0234 0.261 0.0234 0.255 0.0265 Psychologist -0.383 0.7170 -0.386 0.7159 -0.385 0.7161 -0.428 0.6854 Time Trend 0.016 0.0018 0.016 0.0318 0.016 0.0253 0.015 0.0096 X t for treated (y/n) -1.475 0.1250 A-hj/! fo r drug choice -0.020 0.9659 -0.021 0.9608 -0.053 0.8769 R^is adjusted for number of independent variables. AD: antidepressants 71 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.C.2.3.2. Impact of Treatment Selection Bias on Other Parameter Estimates One objective of using treatment selection adjustment term(s) in the subgroup log total costs regression models is to derive the parameter estimates for observation variables controlled for the influence of the unobservable characteristics in the treatment-drug selection process. For the 4 sets of cost models listed in Table 3.C.5A to Table 3.C.5F, the parameter estimates from each of them were called as the OLS estimates, standard single lambda estimates (treated only patients), expanded single lambda estimates (entire MDD population), and double lambda estimates. In general, as opposed to the OLS cost model, there were no significant changes in the parameter estimates across three- treatment selection models for each of the available antidepressant types. These results support the robustness of OLS model specification in the previous study (McCombs et al. 1999). Particular attention was paid to the changes in the inference at the significance level of p-value less than 0.05 across the different models. Among four drug groups (fluoxetine, paroxetine, TCAs, and HCAs) with evidence of treatment selection bias, the results for fluoxetine, paroxetine, and TCAs, will be discussed because none of changes in the inference has been found across the different models for the HCAs patients. For the fluoxetine users, Hispanic ethnicity was shown to use significantly less health care relative to whites in the OLS model (-16.5%, p=0.0456) and the standard single lambda model (-16.4%, p=0.0484). The expanded single lambda and the double lambda models did not show Hispanic ethnicity to significantly reduce health 72 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. care costs. In addition, patients diagnosed as recurrent MDD spent significantly more than the patients diagnosed as single-episode MDD in double lambda method (12.3%, p=0.0466), while the OLS estimates or two single lambda estimates did not show the significant difference between diagnosis codes. Similarly, paroxetine patients with a diagnosis of recurrent MDD increase total costs by 12.2% (p=0.0491) based on the double lambda estimate or by 13.5% (p=0.0272) based on the standard single lambda estimate, or by 13.3% (p=0.0252) based on the expanded single lambda estimate. The results for the patients using TCAs as their initial antidepressants showed that the statistical inference for explanatory variables could vary across the different cost models. Age was not significantly associated with total health care costs in all selection-corrected models relative to a significant and negative age effect found in the OLS model (-22.4%, p=0.0389). Male patients in the TCAs group spent more on health care based on the double lambda estimate (14.5%, p=0.0397) and the standard single lambda estimate (12.7%, p=0.0474) in contrast to the gender effect based on the OLS estimate was not significant (5.9%, p=0.3369). Lower costs for “other” races was found in the OLS model (-22.3%, p=0.0002) and the double lambda model (- 14.7%, p=0.0310). The TCAs patients residing in the rural area exhibited significant cost reduction (-44.1%, p=0.0487) only in the double lambda model. However, the parameter estimates for the historical effect from all selection-correct models were not statistically significant in contrast to the significant OLS estimate (1.5%, p<0.0001). 73 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.C.2.4. Influence of Heteroscedasticity on Double Selection Bias in Total Health Costs Models We further explored the influence of heteroscedasticity on both the treatment initiation or access effects bias and the drug choice or substitution effects bias explicitly represented by the double lambda method. Table 3.C.6 presents the heteroscedasticity-corrected second stage log total costs model, as compared with heteroscedasticity-uncorrected log total costs model. Heteroscedasticity evidently affected the significance of selection bias in the HCAs users and the sertraline users. The correction for heteroscedasticity in the HCAs users resulted in change in the statistical inference to an insignificant and heteroscedasticity-corrected drug choice bias (p=0.1753) from a significant and heteroscedasticity-uncorrected drug choice bias (p=0.0227). After correction for heteroscedasticity in the sertraline users, the p-value associated with treatment initiation bias in sertraline group was no longer significant (p=0.4627), as compared with a marginally significant bias before heteroscedasticity correction (p=0.0523). Fluoxetine users also displayed change in the inference on treatment initiation bias from p value of 0.0401 to p value of 0.0748 after correction for heteroscedasticity. In addition, other antidepressant users also exhibited a big increase in p value from 0.1250 to 0.5152 for treatment initiation bias after correction for heteroscedasticity. The heteroscedasticity affected the other parameter estimates for each of the available drug types as well. The double lambda models for fluoxetine, paroxetine, and sertraline exhibited quite stable because of limited heteroscedasticity impact on 74 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the parameter estimates other than the double lambda terms. For the fluoxetine users or the paroxetine users, diagnosis of recurrent episodes of MDD was not a significant predictor of total health care costs after correction for heteroscedasticity (after: p=0.2985 versus before: p=0.0466 for fluoxetine; after: p=0.0884 versus before: p=0.0491 for paroxetine). For the sertraline users, the historical time trend also became an insignificant predictor of total costs after correction for heteroscedasticity. Correction for heteroscedasticity resulted in many changes in the statistical inference of parameter estimates estimated by double lambda models for TCAs, HCAs, and other antidepressants. Specifically, the effect of male gender, “other” > races, and diagnosis of recurrent MDD episode were not significant in explaining total health care costs associated with initial antidepressant TCAs in the heteroscedasticity- corrected models. For HCAs, even more variables such as all minority groups (black, Hispanic, or “other” race), diagnosis of recurrent MDD, and count of comorbidities lost their prediction power for total health care costs. For other antidepressant users, 6 variables were shown to be not significant after correcting for heteroscedasticity. It was very surprising to find 3 cost variables (hospital, drug, and home health care) in 6 months prior to the other antidepressant therapy were in the list of these 6 variables because usually the prior period costs were very good predictors for total costs in the first post-treatment year. This failure of some types of prior period costs to predict total health care costs might be due to relatively small sample size of patients starting their therapy with other antidepressants because the p values for these 3 cost variables were still very close to the level of 0.05. 75 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. TABLE 3.C.6. Influence of Heteroscedasticity on Parameter Estimates of Total Health Care Costs Models by Drug T y p e _______ _ _ V ariable Fluoxetine Paroxetine Sertraline HCAs Other ADs TCAs Est. P- P- Est. P- Est. P- P~ Est. P- P- Est. P- E st. ........ « _ .. Age -0.172 valuea 0.0821 valueb 0.0828 -0.096 value* 0.3208 valueb 0.3219 -0.176 value* 0.3303 value" 0.4326 -0.273 value* 0.0111 value” 0.0369 0.073 value” 0.7110 value” 0.6576 -0.204 value" 0.0593 value” 0.0700 Agesq 0.021 0.0323 0.0341 0.014 0.1354 0.1321 0.026 0.1185 0.2011 0.032 0.0023 0.0023 -0.001 0.9404 0.9427 0.025 0.0178 0.0175 Gender -0.022 0.7458 0.8035 0.125 0.0857 0.1002 0.242 0.0963 0.3405 -0.088 0.2195 0.5621 0.231 0.0568 0.2753 0.145 0.0397 0.1203 Black -0.058 0.6018 0.7160 0.083 0.4373 0.4758 -0.244 0.3856 0.5576 0.263 0.0063 0.2535 0.406 0.2313 0.3130 0.172 0.0955 0.2727 Hispanic -0.139 0.0976 0.1630 0.002 0.9854 0.9860 0.142 0.4004 0.6613 -0.229 0.0087 0.0763 0.038 0.8071 0.8898 -0.002 0.9841 0.9861 O ther Race -0.031 0.6390 0.7080 0.029 0.6495 0.6636 0.024 0.8338 0.9012 -0.158 0.0067 0.0799 -0.010 0.9352 0.9566 -0.147 0.0310 0.0770 R ural 0.156 0.4003 0.4679 -0.190 0.3681 0.3760 0.344 0.4532 0.5529 -0.061 0.7527 0.7610 -0.749 0.0171 0.2058 -0.441 0.0487 0.0517 Specialist 0.052 0.6222 0.6842 -0.056 0.6163 0.6256 -0.187 0.3844 0.6758 -0.032 0.7704 0.8163 -0.060 0.7848 0.8817 -0.201 0.0880 0.1153 Recur. MDD 0.123 0.0466 0.2985 0.122 0.0491 0.0884 0.048 0.6687 0.9006 0.143 0.0101 0.0906 0.114 0.3387 0.7256 0.155 0.0079 0.0361 # Concom Rx 0.060 0.2014 0.3267 0.022 0.6617 0.6758 0.071 0.3726 0.7215 -0.006 0.9056 0.9249 0.123 0.1075 0.3823 0.076 0.0856 0.1452 #of Dx 0.035 0.0029 0.0381 0.040 0.0028 0.0066 0.039 0.0849 0.5278 0.027 0.0278 0.4294 0.052 0.0210 0.3557 0.042 0.00)7 0.0040 One Pharm -0.318 0.0028 0.0030 -0.307 0.0040 0.0038 0.219 0.3052 0.3580 -0.381 0.0008 0.0006 -0.094 0.6182 0.5851 -0.114 0.3537 0.3357 Hospital 0.055 0.0000 0.0000 0.064 0.0000 0.0000 0.013 0.5556 0.6642 0.062 0.000) 0.0000 0.107 0.0127 0.0725 0.069 0.0000 0.0000 Ambulatory 0.138 0.0000 0.0000 0.135 0.0000 0.0000 0.123 0.0000 0.0000 0.145 0.0000 0.0000 0.101 0.0000 0.0000 0.149 0.0000 0.0000 Drug 0.250 0.0000 0.000) 0.316 0.0000 0.0000 0.457 0.0005 0.0015 0.317 0.0000 0.0000 0.140 0.0480 0.1099 0.206 0.0000 0.0000 Home Health 0.195 0.0000 0.0000 0.263 0 . 0 0 0 0 0.0000 0.149 0.0141 0.0242 0.229 0.0000 0.0000 0.255 0.0265 0.0518 0.244 0.0000 0.0000 Psychologist 0.548 0.5295 0.5220 1.105 0.1424 0.1362 -1.698 0.2563 0.3336 -0.391 0.4246 0.4465 -0.428 0.6854 0.7357 0.452 0.5043 0.5064 Time Trend 0.013 0.0000 0.0003 0.009 0.0081 0.0121 0.012 0.0037 0.2946 0.012 0.0004 0.0098 0.015 0.0096 0.1088 0.006 0.1687 0.1705 X t for -0.662 0.0401 0.0748 0.347 0.3279 0.3446 -1.442 0.0523 0.4627 0.012 0.9720 0.9820 -1.475 0.1250 0.5152 0.253 0.4886 0.5330 treated (y/n) X r v i for 0.104 0.7372 0.8232 0.116 0.7296 0.7955 -0.023 0.9418 0.9812 -0.737 0.0227 0.1753 -0.053 0.8769 0.9619 -0.620 0.0042 0.0485 drug choice ^ _ _ ^ ™ a : not corrected for heteroscedasticity; corrected for heteroscedasticity Est.: Parameter estimates; Recur. MDD: recurrent MDD diagnosis; # Concom Rx: number of concomitant drugs; # of Dx: number of concomitant drugs; # of Dx: number of comorbidities; One Pharm: single pharmacy use. 76 3.C.2.5. Double Selection Bias in Cost Models by Type of Service Health care costs were also divided by types of services, including ambulatory service, hospital care, long term care, home health care, other services, and prescription drug. As extensions to total costs regression models adjusted by double lambda terms, health care cost by type of service were also analyzed by subgroup regression models using double lambda terms. Unfortunately, Table 3.C.7 presents very limited information on double selection bias by type of service for each antidepressant (any p-value less than 0.10 was identified). Based on the cost model using double-lambda method with correction for heteroscedasticity, drug choice bias in modeling the other unspecified cost was found in the fluoxetine regression models (2.74, p<0.10) in addition to the treatment initiation bias in modeling total costs as discussed before. Neither the paroxetine users nor the sertraline users were associated with treatment selection bias in modeling any type of cost. HCAs antidepressants used as initial antidepressant therapy were associated with the drug selection bias in modeling home health care cost (-5.80, p<0.10). Interestingly, both treatment initiation bias (-5.11, p=0.0208) and drug choice bias (-1.71, p=0.0284) were found in the ambulatory cost model for the other antidepressants users. Similar to the results for total costs, TCAs were associated to the significant drug choice bias affecting total costs (-0.620, p=0.0485), net costs (- 0.96, p=0.0210) and other unspecified cost (2.83, p=0.0304). There was the treatment initiation bias affecting drug cost as well (1.07, p=0.0696). 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE 3.C.7. Treatment Selection Bias on Health Care Cost Models by Drug Type and by Type of Service in California Medicaid Program _________________________________ _ Type of service Fluoxetine Paroxetine Sertraline HCAs Other ADs TCAs Total Costs Est. P- value Est. P- value E st P- value Est. P- value E st P~ value Est. P- value IMR for treatment -0.662 0.0748 0.347 0.3446 -1.442 0.4627 0.012 0.9820 -1.475 0.5152 0.253 0.5330 IMR for drug choice 0.104 0.8232 0.116 0.7955 -0.023 0.9812 -0.737 0.1753 -0.053 0.9619 -0.620 0.0485 Ambulatory IMR for treatment -0.648 0.5195 -0.109 0.9343 -2.556 0.4007 0.178 0.8652 -5.109 0.0208 0.095 0.9294 IMR for drug choice -0.310 0.7588 -1.210 0.2278 0.905 . 0.6234 0.731 0.4370 -1.713 0.0284 -0.697 0.2960 Drug IMR for treatment -0.069 0.9047 -0.520 0.5135 -0.180 0.8770 -0.009 0.9884 0.842 0.7104 1.067 0.0696 IMR for drug choice 0.028 0.9595 0.819 0.2551 0.226 0.6519 -0.684 0.2657 -0.821 0.2976 -0.205 0.6592 Hospital IMR for treatment -0.906 0.6031 4.124 0.1536 3.597 0.4781 0.661 0.7362 -4.419 0.5869 2.674 0.1367 IMR for drug choice 0.803 0.6296 -2.666 0.5216 -2.431 0.3963 -1.613 0.4316 -0.168 0.9632 -0.788 0.5550 LTC IMR for treatment -0.392 0.4560 -0.535 0.4659 -0.504 0.7071 -0.489 0.4152 0.432 0.8094 -0.834 0.1881 IMR for drug choice 0.602 0.1657 -0.293 0.7171 -0.176 0.7500 -0.184 0.7475 -0.431 0.4916 -0.392 0.3630 Home Health IMR for treatment 1.581 0.3114 -0.392 0.8313 -0.219 0.9477 -0.816 0.8274 4.542 0.5378 -0.171 0.9162 IMR for drug choice -1.048 0.5004 1.986 0.1240 0.458 0.7477 -5.803 0.0848 -0.459 0.8923 -3.903 0.0062 Other IMR for treatment 0.345 0.8700 1.455 0.4860 -4.356 0.5199 3.807 0.0742 -0.101 0.9847 0.224 0.9012 IMR for drug choice 2.741 0.0817 2.232 0.2283 -0.293 0.9274 -1.337 0.6978 2.645 0.1342 2.834 0.0304 NetRx IMR for treatment -0.694 0.1703 0.479 0.3669 -1.975 0.4615 0.105 0.8677 -1.981 0.5122 -0.102 0.8548 IMR for drug choice -0.010 0.9870 0.067 0.9176 0.009 0.9950 -0.711 0.2691 -0.076 0.9587 -0.961 0.0210 *: p<0.10 **: p<0.05 ***:p<0.01 ****: pcO.QQl All estimates have been adjusted for heteroscedasticity. Est.: coefficients for double lambda terms 3.C.2.6. Comparative Logarithm Transformed Cost Effects by Type of Service across the Alternative Drugs Relative to No Therapy Any attempt in the ITT models to measure the relative cost effects of alternative medications using data from real-world treatment settings must take into account the potential for treatment selection bias created by the purposeful selection of specific drug therapies by the physician to address the patient’s needs. As a result, the treatment selection process may result in differences between treatment groups that affect the health care costs being used to evaluate the cost effects of the alternative 78 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. products. While multivariate statistical models can control for observable differences between treatment groups, there is always the nagging concern that unobservable differences exist between groups that escape detection, thus resulting in biased estimates. The ITT models can be incorporated with treatment selection bias methods to control for the treatment selection bias due to the unobservable factors in the selection process across the alternative antidepressants as well as the option of no antidepressant therapy. The treatment selection bias methods are the expanded single lambda method to account for single-stage decision and the double lambda method to account for sequential decisions in the entire depressant patients. In general, as compared to the untreated population, the medication therapy using all available antidepressants (TCAs, HCAs, fluoxetine, paroxetine, sertraline, and other new antidepressants) was associated with reduction in total costs before and after the formulary expansion. The results are presented in Table 3.C.8 for the single lambda method and in Table 3.C.9 for double lambda method. The estimated reduction in total costs was primarily attributed to the savings in ambulatory cost and home health care. The results for the 111 model using the single lambda method are presented in Table 3.C.8. Assuming that the results for the TCAs reflected mostly the substitution effects, the results appear to show that the effectiveness of the TCAs on total direct health care costs improved after the formulary expansion. This increased effectiveness resulted from shifting more severely ill patients to paroxetine or fluoxetine in the post- 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. expansion period. Conversely, the results for the HCAs and sertraline did not demonstrate the increased effectiveness. However, none of the above results from the single lambda method reached the statistical significance. Overall, the single lambda adjustment was an effective way to control for the substitution effects. TABLE 3.C.8. Comparative Cost Effects of Alternative Initial Drugs with Single Lambda Adjustments before/after the Formulary Expansion by Type of Service (No Antidepressant Therapy as the Comparison Group) ' ____________________ __________ Tricyclic Antidepressants (TCAs) Heterocyclic Antidepressants Other Antidepressant Before After Before After Before After Total Costs -1353“ -1759 -1723 -395d -3060 -1091 Ambulatory -1217a -1746 -1205 -1531 -2332 -479 Drug 33 19 172 00 340 00 iH Hospital 24 -13 -414 257 -286 576 LTC 66 22 22 12 -101 102 Home Health -23 l a 25b -260 -215 -67 T -346 Other -22 -60 -31 2 -1 -2 NetRx -1386a -1779 -1895 -543“ -3400 -1280 Fluoxetine Paroxetine Sertraline Before After Before After Before After Total Costs -1173 -567 -2614 -749 -2118 -1852 Ambulatory -2063 -400 -2445 -444 -2144 -1617 Drug 1032° 387d 577° 234 282 180 Hospital 58 -67 -236 -39 235 -380 LTC 105 25 -19 62 -99 40 Home Health -277 -188 -475 -171 -346 -302 Other -19 -4 0 -5 -35 -74 NetRx -2205 -953 -3191 -983 -2400 -2032 a. Statistically significant relative to no drug therapy b. Statistically significant difference for TCAs relative to TCAs in baseline period. c. Statistically significant for alternatives relative to TCAs in baseline period. d. Statistically significant difference for alternatives relative to alternatives in baseline period. The results for the ITT models using the double lambda method for controlling for the confounding access and substitution effects are displayed in Table 3.C.9. It appears that this statistical approach may have been at least effective in controlling for the substitution effects. The effectiveness of the TCAs compared to no drug therapy increased after the formulary expansion, but increased effectiveness was not 80 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. statistically significant. However, the HCAs patients exhibited a reduction in cost savings in the post period (from -$2,749 to -$1,930 p<0.05) and sertraline savings were unchanged after the formulary expansion. Assuming for the moment that the substitution effects is adequately controlled for by the double lambda method, then the observed difference in the pre- and post expansion effectiveness of fluoxetine and paroxetine would only reflect the access effects. The change (from -$1,821 to -$2,070) in the effectiveness of fluoxetine in the post-expansion period relative to no drug therapy are consistent with the intuition that the access effects consisted of less severely ill and less costly patients on fluoxetine after the formulary expansion. Specifically, this product appears to be more effective in the post period, though differences are not statistically significant with the exception of reduced duration of therapy (not reported here). Again the change (from -$2,857 to -$2,259) in the effectiveness of paroxetine in the post-expansion period did not agree with the direction of change for fluoxetine. This suggested that the access effects resulted in more severely ill patients on paroxetine after the formulary expansion. Finally, it is interesting to note that both fluoxetine and paroxetine exhibit roughly equivalent savings in net costs and total costs in the post period relative to no therapy, regardless of the treatment selection adjustment method taken and apparent shifting of more severely ill patients form conventional antidepressants. While some of the improved effectiveness is likely due to the access effects attracting less severely ill and less costly patients into active drug therapy, the overall cost of treating 81 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. depression did not increase with expanded access to the more expensive antidepressants. TABLE 3.C.9. Comparative Cost Effects of Alternative Initial Drugs with Double Lambda Adjustments before/after the Formulary Expansion by Type of Service (No Antidepressant Therapy as the Comparison Group) _____________________________________ Tricyclic Antidepressants (TCAs) Heterocyclic Antidepressants Other Antidepressant Before After Before After Before After Total Costs -231 l a -2877 -2749 -1930d -3102 -2300 Ambulatory -665 -990 -622 -391 -941 -1130 Drug -333 -435 -217 -317 -36 -272 Hospital -1589 -2125 -2160 -1849 -2251 -1641 LTC 237 255 209 194 142 310 Home Health 6 405b 11 396 -58 403 Other 41 23 39 46 54 39 NetRx -1979 -2443 -2533 -1614d -3067 -2029 Fluoxetine Paroxetine Sertraline Before After Before After Before After Total Costs -1821 -2070 -2857 -2259 -2897 -2834 Ambulatory -1059 -535 -1163 -647 -1256 -728 Drug 620° -66d ) — ± O O n -220 -130 -259 Hospital -1975 -2097 -2256 -2074 -1750 -2519 LTC 341 198 226 236 127 243 Home Health 211 400 109 417 87 475 Other 53 37 62 35 38 -40 NetRx -2442 -2005 -3042 -2040 -2768 -2575 a. Statistically significant relative to no drug therapy b. Statistically significant difference for TCAs relative to TCAs in baseline period. c. Statistically significant for alternatives relative to TCAs in baseline period. d. Statistically significant difference for alternatives relative to alternatives in baseline period. 82 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.D. Discussion The objectives of this study were to evaluate the impact of the formulary expansion on the treatment-drug selection process across alternative antidepressant therapies as well as no antidepressant therapy, and to evaluate the impact of the unobservable factors in the choice process on modeling total health care costs by utilizing alternative treatment selection models. From the perspective of the formulary • change, this study also compared cost effects associated with each individual antidepressant before and after formulary expansion relative to no antidepressant therapy. To accomplish the objectives, several aspects of the study were carefully considered for better utilization of the available information in the 100% MDD patient population. 3.D.I. Methodological Issues This study differentiated from the other studies (Hylan et al. 1998; Edgell et al. 1998; Bemdt et al. 2000) in the structure of choice model (single-stage versus two- stage multinomial choice model). The two-stage treatment-drug choice with the multiple alternative options reflects the clinical decision process of whether to seek treatment and which drug to use as the initial drugs, if treated. This two-stage treatment-drug model was necessitated by the fact that the treatment selection process was significantly altered by a formulary change of adding fluoxetine and paroxetine into the Medi-Cal drug formulary that occurred in the study period. Conceptually, this formulary expansion created the access effects and substitution effects related to the decision to seek treatment and the drug choice, respectively. As a result, the variable 83 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. of the formulary change was included in the two-stage treatment-drug choice model (double selection criteria) to derive double lambda terms related to the decision to seek treatment (the access effects), and the drug choice (the substitution effects). With the double lambda terms accounted for the changes in the unobservable variables created by the access effects and substitution effects on health care costs, the double lambda method developed by Viverberg (Viverberg, 1993; Viverberg, 1995) was ultimately applied in the Medi-Cal data to model total health care costs. One keynote to this double lambda method is that one can not adequately deal with treatment selection bias through correction for the drug choice by itself, or a mixture of the decision to seek treatment and the drug choice together by means of the single lambda method. The double lambda method separates the bias by better using the formulation of clinical selection process in its nature. The approach gives health outcomes researchers better chances to find the significance of selection bias, especially when two kinds of biases are in the opposite direction. Intuitively, as compared to Figure 2.C.1, the selection process rule in Figure 2.B.2 implicitly represents an amalgam of random factors determining both the decision to seek treatment and the drug choice. In other words, the treatment selection in Equation (2.B.2.) shows a mixture of the two decisions of treatment selection: the decision to seek treatment and the choice of alternative drugs, if treated. In fact, if the effects of these two kinds of treatment selection are in the opposite direction, one will likely find the coefficient for the single lambda term, suggesting lack of any treatment selection bias. This superiority was especially demonstrated in Table 3.C.5B for the fluoxetine 84 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. users. The coefficients for the selection bias adjustment term(s), present a significant negative treatment initiation bias and an insignificant positive drug choice bias while neither of single lambda estimates showed any evidence of statistical significance. From the perspective of formulary policy analysis, if only the single lambda method was employed, there was neither clear interpretation for the impact of the formulary expansion (i.e., the access effects or the substitution effects) on treatment selection, nor the specific measurement of treatment selection bias associated with either the access effects or the substitution effects. Another keynote to this double lambda method is the importance of including the MDD patient with no antidepressant therapy for the analysis of the access effects. Excluding the untreated patients in an analysis would only be valid when the analysis would be done in the constant treated population without shifting previously untreated MDD patients to the treated sample. This MDD data clearly demonstrated that the formulary expansion created the significant and immediate access effects. In addition, physicians were more likely to diagnose MDD after gaining the access to the added SSRIs. For the fluoxetine patients, compare the results of double lambda method with the results of single lambda method using treated population suggested that it might not be possible to remove the influence of the access effects by excluding the untreated patients from the analysis. In this Medi-Cal MDD sample, the proportion of “no therapy” was about 20% of the depressed population, which also legitimated the inclusion of untreated patients into the study. In other antidepressant studies, the inclusion of “no therapy” patients was of interest until a couple of studies using the 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. “no therapy” as reference group was found a strikingly high percentage (53%) of “no therapy” group in the sample with diagnosis of depression (Sturm and Wells, 1995; Edgell et al. 2000). This study using data from October 1994 and January 1998 resolved the channeling bias across three major SSRIs: fluoxetine, paroxetine, and sertraline, which were well-established antidepressants during that time period. A number of recently published studies using retrospective data have employed the methods for correcting for treatment selection bias to address the nonrandom patient assignment issue. Hylan et al reported results from a publicly available retrospective claims database (Market- Scan™) to compare the differences in mental health care costs, non-mental health care costs, and total costs among three SSRIs: fluoxetine, paroxetine, and sertraline. In the study, a standard single lambda method was highlighted for an attempt to account for nonrandom treatment choice (Hylan et al. 1998). The application of treatment selection procedure in the Hylan et al study was challenged by possible channelin g bias because the study period covered from 1990 to 1994, when paroxetine and sertraline were the newly launched antidepressants at that time. As Bemdt et al commented on Hylan’s study, this incorporation of data from a time period when not all choices were available undermines the attempt to control for sample treatment selection (Egberts et al. 1997; Bemdt et al. 2000). Bemdt also challenged the result of the sample treatment selection procedure, which was statistically significant only for fluoxetine saying that the result was possibly attributable to this channeling bias (Bemdt et al. 2000). To address channeling bias, Bemdt et al study employed the 86 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. same (Market Scan™) data but from more recent years from 1995 to 1996 to proceed the sensitivity analysis of two-stage treatment selection method. In contrast to Hylan et al, it was found that selective, nonrandom SSRI choice is not correlated with total depression-related and total health care expenditure. However, as Bemdt stated in the paper “this absence of evidence is not necessarily evidence of absence”, the extent to which the specification in his model controls reliably for nonrandom selection remains a matter of some controversy. In Bemdt et al study, model identification is attained in part by excluding the diagnosis code, prior period psychotherapy, and prior period hospitalization variables from the second stage as suggested in Little et al study (Little, 1985). However, in the Bemdt et al study these variables were not tested whether they were statistically significant predictors of health care costs before utilizing them as instrumental variables. This raised uncertainty of model identification for the claimed absence of selection bias. In the model estimation of the Bemdt et al study, to accommodate possible heteroscedasticity in the treatment selection models, the White procedure (White, 1980) for computing heteroscedasticity-robust standard errors was employed in addition to the log-transformation of cost data. The White procedure is widely used in regular OLS procedure based on the OLS assumption of random independent sample. However in the case of nonrandom assignment in the treatment selection models, the random independent sample was violated, therefore it was not appropriate to apply the White procedure to obtain the correct standard error for parameter estimates. Actually, the nature of treatment selection requires an additional source of variation in 87 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the correlation of selection process and correlation across observations. Heckman et al has shown that the asymptotic variance can be achieved by adding a term accounting for the additional variation (Heckman, 1979). The variance/standard error correction method proposed by Heckman became a norm of dealing with heteroscedasticity in treatment selection models. Furthermore, it was expanded to the selection process for two-by-two choice model (Maddala, 1983) and was then modified for double selection criteria with multiple alternatives (Viverberg, 1993; Viverberg, 1995) to obtain the correct standard deviation for parameter estimates. These results from comparing heteroscedasticity-corrected p value with heteroscedasticity-uncorrected p value signified the importance of heteroscedasticity correction for right inference. In this MDD study, the results of heteroscedasticity-corrected p value estimated by an adaptation of Viverberg’s method suggested that the heteroscedasticity affected the inference on the double treatment selection bias, especially in sertraline group. The comparative cost effects for all available antidepressants in the ITT models relative to the untreated MDD patients has been performed in the framework of treatment effects model. The treatment effects model with adjustment of treatment selection bias was developed by Bamow et al to study the returns to education where the indicator variable was used to indicate the presence of a treatment, for example, going to college (Bamow, 1981). In this MDD study, as opposed to the option of no antidepressant therapy, this treatment effects model was expanded to accommodate for the multiple alternatives and treatment selection bias. The results suggested that the model adjusted by either single or double selection bias has shown quite similar results 88 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. for both double lambda and single lambda methods correcting for treatment selection bias. The comparative cost for all available antidepressants can also be model as the expected cost of the alternative less the expected cost of the reference group (Munane et al. 1985; Hylan et al. 1998; Edgell et al. 2000). This approach was complex not only in constructing the difference in the expected costs for the comparison groups but also in a very large variance for the expected cost difference. In addition, multiple pairwise comparisons need be adjusted for the inflated alpha bias. For example, this study requires at least 6 pairwise comparison for each drug group as opposed to the untreated patients. Therefore, the adjusted significance level is about 0.008. Preliminary results have shown that there was insignificant cost difference for any comparison conducted relative to TCAs (not reported here). 3.D.2. Impact of the Formulary Expansion on Two-Stage Treatment Selection Process and Parameter Estimates for Total Health Care Costs Model The formulary expansion was designed to change treatment decisions by expanding the clinician’s options to prescribe fluoxetine and paroxetine. It is conceivable that a whole set of physician behavior and/or patient behavior have changed, directly or indirectly in response to this formulary policy change. Some new patients were served, primarily with these two added SSRIs (access effects), and some existing patients substitute the added SSRIs for other products. The access effects and substitution effects of the formulary expansion resulted in a significant and sustained increase in number of patient-episodes using fluoxetine or paroxetine as the initial 89 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. drug without corresponding decrease in using other major antidepressants with the exception of gradually reduction in the use of TCAs (McCombs et al. 2001). In addition, our data clearly document three interesting findings in the changes of initial drug choice before and after the formulary expansion. First, in contrast to the fact that there was a trend of downsizing Medi-Cal FFS beneficiaries, there was an expanding population of patients who had a MDD diagnosis over time. This may reflect a growing awareness by the general practitioners of major depression, or an increased willingness to record MDD as a diagnosis after gaining access to fluoxetine or paroxetine. This is also consistent with other studies which found that depression was underdiagnosed and undertreated by primary care and nonpsychiatric practitioners despite high prevalence of depressive symptoms and major depressive episodes among patients of all ages (AHCPR, 1993). The Medi-Cal trend may also reflect the trend of socially de-stigmatizing depression in that more previously undiagnosed/untreated patients starting engaging in health care systems. Second, treatment decision to use of fluoxetine and paroxetine was very sensitive to formulary status change because of sudden and sustained increase in MDD patients initiating therapy with fluoxetine and paroxetine immediately after the two drugs were added into the Medi-Cal drug formulary. Apparently the clinicians were well informed about the formulary expansion. After controlling for patient demographics, clinical attributes, prior health care utilization, and an exogenous time trend in this Medi-Cal sample, the double lambda method provided some evidence of treatment selection bias in the decision to seek 90 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. treatment, especially in the patients starting their medication with fluoxetine. The direction of estimate for the treatment initiation bias was explained as that without adjustment for the double selection bias, the total health care costs associated with fluoxetine use would be higher compared with the total costs estimated from a randomized sample. This result from bias direction was consistent with Hylan et al study (Hylan et al. 1998). The relationship between the decision to seek treatment and the access effects led to the hypothesis that the access effects predominately affect the fluoxetine group to allow the relatively less ill patients to receive medication, especially fluoxetine. The hypothesis could be supported by the evidence that the patients using fluoxetine as initial therapy after the formulary expansion tended to be utilizing relatively less health care based on 6-month cost data prior to starting the fluoxetine treatment in the light of the level before the formulary expansion and the general historical effect. Therefore, it might be logically observed the relatively lower total 1-year post-treatment health care costs. This downward projection for total costs in post-treatment period was enforced because total health care costs in the post treatment for these patients would be even smaller than the actually observed level if treatment initiation bias would be accounted for by the adjustment term, or in other words, patients would be randomly selected. However, although paroxetine was also added to the Medi-Cal drug formulary, the pattern for the estimated treatment selection bias in paroxetine users was not similar to fluoxetine in all three types of treatment selection model. There was a significant drug choice bias in the paroxetine-treatment population estimated by 91 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. excluding the untreated population in the cost model. Given that the paroxetine- treated patients after the formulary expansion tended to increase their health care utilization, it appears that the paroxetine patients would cost more in the post treatment period than the actually observed level if the drug choice bias as well as the substitution effects would be corrected for. Unfortunately, no detailed comparison between these two added drugs could be made due to limitation in the information of patient severity in Medi-Cal paid claims data. The double lambda estimation method for TCAs signified the drug choice bias, which was involved with the substitution of the added SSRIs for TCAs in the relatively severely ill patient population after the formulary expansion. Combined with the results for fluoxetine and paroxetine, the substitution effects appeared to shift the relatively severely ill patients primarily to paroxetine. 3.D.3. Policy Implications of Adding Two SSRIs to the Medi-Cal Formulary Increases in the cost of drug therapy have led to the design of many management techniques aimed at reducing cost by restricting physicians’ prescribing autonomy. Many Medicaid programs have established limited formularies and often require prior authorization for nonlisted drugs or therapeutic substitution of a listed agent when a nonlisted drug has been prescribed. Drug formularies in Medicaid programs are also used to leverage pharmaceutical companies to sell their products at discounted price in exchange for formulary status. Unfortunately, the state legislatures, HMOs, and health policy makers have often implemented drug regulations with little empirical evidence about their true impact. 92 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Previous studies reported increase in total resource use when restrictions were placed on the number of monthly reimbursement for prescriptions in Medicaid programs or formulary limitation in expansive drugs (Soumerai et al. 1987; Soumerai et al. 1991; Soumerai et al. 1994; Kozma et al. 1990; Moore et al. 1992, Dranove et al. 1989; Moore et al. 1993; Martin and McMillan, 1996). Previous studies on NSAIDs use in a Medicaid program did not support the concern that implementation of prior- authorization policy or formulary limitation adversely affected the cost effectiveness of drug therapy (Smalley et al. 1995). However, these results of formulary limitation or prior-authorization policy implementation might not be able to answer the question of the formulary expansion. It was found that in a private practice clinic, patients with 2 SSRIs on their drug formulary had better treatment completion rates than patients with only 1 SSRI in their drug formulary (Streja et al. 1999). A study using the same Medi-Cal data used here found no improvement in treatment completion rate after the formulary expansion, likely due to the access effects of this formulary expansion (McCombs et al. 2001). This result is not inconsistent with prevailing economic theory based on findings that greater choice enhances consumer satisfaction and economic efficiency. It is not surprising, however, the formulary expansion of fluoxetine and paroxetine in Medi-Cal has a collective aspect that can result in quite unanticipated global changes in the antidepressant therapy, often counter to our intuition. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.D.4. Limitations of This MDD Study Several aspects of this study may be deemed to be limitations and need to be addressed. This study only addressed the direct health care costs incurred by patients initiating therapy for depression, which might be appropriate from the perspective of Medi-Cal. From the societal perspective, in addition to direct costs, the indirect costs of treating MDD might be larger than direct costs based on the data of economic burden of depression (Greenberg et al. 1993). This study did not have the information on potentially very significant benefits such as quality of life improvement, functional and work productivity as well (Finkelstein et al. 1996). In addition, this study did not analyze the long-term treatment (>12 months) outcomes such as symptom relapses and episode recurrence. Because of the retrospective nature of this analysis, treatment comparison groups were based on an intent-to-treat basis. That is, patient outcomes were compared based on the initial therapy received by a patient. Such a design is useful in a retrospective analysis, in which one wishes to assess the impact of initial treatment selection. However, in the intent-to-treat design, the health care costs are supposed to be attributable to a specific treatment. However, the costs might be by large driven by events occurred later in the treatment episode such as treatment switching, treatment augmentation, and non-compliance, each of which is an outcome in its own right. Although special attention has been paid on enhancing model identifiability for selection bias as discussed in model specification, the results did not find much 94 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. evidence of selection bias. For example, in the fluoxetine group, only marginal significance was found in modeling total costs after correction for heteroscedasticity. Claims or billing data rarely contain the clinical information on clinical severity or functional outcomes necessary to detect or adjust for potential biases. Data compiled for billing or claims purposes are often limited by significant errors and omissions in clinical important areas (Jollis et al. 1993). Prospectively collecting the information in a “real word” practice can be used to provide more rigorous answers to such policy issues as when beginning antidepressant treatment, which eventually results in the best clinical, functional, and economic outcomes, and how the effectiveness of antidepressant treatment changed with formulary policy change (Simon et al. 1995b). Finally, the inverse Mill’s ratio version of the treatment selection models raise the problems of re-transforming the log dependant variable because the use of the inverse Mill’s ratio actually induce heteroscedasticity in the error term (Manning, 1998). The use of a log transformed dependent variable from highly skewed data such as labor wage and health care expenditure, has become commonplace in applied econometrics (Manning, 1998). One widely used rationale for the log transform derives from the single parameter Box-Cox model dealing with the issue of skewed or non-normal data (Box and Cox, 1964). Another issue is due to the heteroscedasticity of error term in treatment selection models. Smearing estimators were the common approach to retransform the log dependant variables with heteroscedasticity of error term (Duan, 1983). Although the correct estimate of true error variance can be 95 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. estimated by using formula as in the appendix, the true error terms is still possible heteroscedastic, then one must incorporate an additional correction to obtain the expected value of health care costs. Vella et al attempted to generate conditional expectations from treatment selection bias models (Vella, 1988), but later it was found that his model only works under very restrictive assumptions (Schaffner, 1998). Lee et al attempted to provide general formula for the computation of expected values of not chosen alternative in treatment selection model with polychotomous choices (Lee, 1995). However, no application has been found using Lee et al proposed method so far. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.E. Conclusions Despite the limitation of the present study, the findings in this MDD study warrant attention. The double lambda method is a new method to account for the treatment selection bias that results from a two-stage treatment-drug choice process with multiple alternatives. This technique was demonstrated for a case study of antidepressant therapy, where the clinical decision process included two-stage, yet correlated choices: the decision to seek treatment and which drug to initiate the therapy, if treated. This method separates the selection bias according to the formulation of treatment selection. In general, the treatment selection bias through the decision node of treatment initiation co-existed the one through drug choice. In contrast, neither of the alternative selection models using the single-stage choice structure could reveal this implication. This study revealed the significance of the access effects and substitution effect of the formulary expansion by incorporating the data from the prior-FE period. This study also expanded our understanding about underdiagnosed and undertreated nature of major depression population by incorporating the untreated patients into the analysis sample. Furthermore, the double lambda method also revealed different pattern in dual selection bias between fluoxetine and paroxetine. As a result, the double lambda method was of value as an alternative estimation strategy for future empirical studies. Adding fluoxetine and paroxetine into Medi-Cal drug formulary had a global, yet unevenly distributed impact on the selection process of initial antidepressants and health care costs associated with each type of the initial antidepressants in an intent-to- 97 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. treat design. After gaining better access to fluoxetine and paroxetine, an expanded population of depression was treated in Medi-Cal program, primarily due to significant increases in patient-episodes using fluoxetine and paroxetine as initial drugs. The concurrently reduced likelihood of using TCAs revealed a significant substitution of SSRIs for TCAs. After controlling for patient demographic, clinical attributes, prior health care utilization in the models of total health care costs, TCAs were found the evidence of significant selection bias due to drug choice by double lambda method. While fluoxetine was associated with a significant selection bias due to treatment initiation process, there was relatively weak evidence of significant selection bias for paroxetine by modeling the treatment selection process of a single- step choice in the treated patients. These findings differentiated the two added antidepressants in the impact of the unobservable factors in the choice process of both the treatment initiation and the drug choice on total health care costs. As opposed to the untreated population, medication therapy using all available antidepressants displayed reductions in total health care costs. The overall cost of treating depression did not increase with expanded access to the more expansive antidepressants. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Reference: AHCPR. Clinical Practice Guidelines: Depression in primary care: detection, diagnosis, and treatment. Rockville (MD): Department of Health and Human Services, AHCPR Publication No. 93-0552, 1993 Anderson C. Measuring what works in health care. Science 263: 1080-1082, 1994 Anderson IM, Tomenson BM, Martindale JJ. Treatment discontinuation with selective serotonin reuptake inhibitors compared with tricyclic antidepressants: a meta-analysis. British Medical Journal 310: 1433-1438,1995 Angst J. Epidemiology of depression. Psychopharmacology 106: S71-74,1992 Bamow B, Gain G, Goldberger, A. Issues in the analysis of selectivity bias. In Stromsdorger E, and Farkas G eds., Evaluation Studies Review Annual, vol 5, Bevlerly Hills: Sage Publications, 1981 Ben-Akvia M, Lerman SR. Discrete choice analysis: theory and application to travel demand. Cambridge (MA): MIT Press, 1985 Bennie EH, Mullin JM et al. A double-blind multicenter trial comparing sertraline and fluoxetine in outpatients with major depression. Journal of Clinical Psychiatry 56: 229-237,1995 Bentkover JD, Feighner JP. Cost analysis of paroxetine versus imipramine in major depression. Pharmacoeconomics 8: 223-232,1995 Bemdt ER, Russell JM, Miceli R, Collucci SV, Xu Y, Grudzinski AN. Comparing SSRI treatment costs for depression using retrospective claims data: the role of nonrandom selection and skewed data. Value in Health 3(3): 208-221, 2000 Box G, Cox D. An analysis of transformations. Journal of the Royal Statistical Society Series B: 211-264, 1964 Crown WH, Obenchain R JL , Englehart L, Lair T, Buesching DP, Croghan T. The application of treatment selection models to outcomes research: the case of evaluating the effects of antidepressant therapy on resource utilization. Statistics in Medicine 17: 1943-1958,1998 De Vane CL. Pharmacokinetics of the newer antidepressants: clinical relevance. American Journal of Medicine 97 (suppl): 135-235,1994 99 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. De Wilde J, Spiers R, Mertens C, Bartholome, Schotte G, Leyman S. A double-blind, comparative, multicentre study comparing paroxetine with fluoxetine in depressed patients. Acta Psychiatrica Scandinavica. 87(2): 141-5, 1993 Danzon, PM, Lillard LA. The resolution of medical malpractice claims-modeling the bargaining process. R-2792-ICJ, The Institute for Civil Justice, Rand Corporation, Santa Monica, 1982 Donoghue J, Tylee A, Wildgust H. Cross sectional database analysis of antidepressant prescribing in general practice in the United Kingdom, 1993-5. British Medical Journal 313: 861-862, 1996 Donoghue JM, Tylee A. The treatment of depression: prescribing patterns of antidepressants in primary care in the UK. British Journal of Psychiatry. 168: 164-168, 1996 Drannove D. Medicaid drug formulary restrictions. Journal of Law Economics 32: 143-162, 1989 Duan N. Choosing between the sample-selection model and the multi-part model. Journal of Business and Economic Statistics 2: 283-289, 1984 Edgell ET, Hylan TR, Draugalis JR, Coons SJ. Initial treatment choice in depression impact on medical expenditures. Pharmacoeconomics 17(4): 371-382, 2000 Egberts AC, Lenderink AW, de Koning FH, Leufkens HG. Channeling of three newly introduced antidepressants to patients not responding satisfactorily to previous treatment. Journal of Clinical Psychopharmacology 17(3): 149-155, 1997 Eisenberg L. Treating depression and anxiety in primary care. Closing the gap between knowledge and practice. New England Journal of Medicine. 326(16):1080-4, 1992 Ernest H, Bennie MB et al. A double-blind, multicenter trial comparing sertraline and fluoxetine in outpatients with major depression. Journal of Clinical Psychiatry 56: 229-237, 1995 Finkelstein SN. Bemdt ER. Greenberg PE. Parsley RA. Russell JM. Keller MB. Improvement in subjective work performance after treatment of chronic depression: some preliminary results. Chronic Depression Study Group. Psychopharmacology Bulletin. 32(l):33-40, 1996 100 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Freemantle N, House A, Song F, Mason JM, Sheldon TA. Prescribing selective serotonin reuptake inhibitors as strategy for prevention of suicide. British Medical Journal 309: 249-253,1994 Greene WH. Treatment selection bias as a specification error: comment. Econometrica 49: 795-798,1981 Greene WH. Econometric analysis 3rd ed. Prentice-Hall, Inc. (NJ) 1997 Greene WH. Limdep Version 7.0 Bellport(NJ): Econometric Software, Inc., 1998 Greenberg PE, Stiglin LE, Finkelstein SN, Bemdt ER. The economic burden of depression in 1990. Journal of Clinical Psychiatry 54: 405-418, 1993 Hay JW. Treatment selection bias in a simultaneous logit-OLS model: physician specialty choice and specialty income. Dissertation, Yale University, 1980 Hay JW, Leu R et al. Ordinary least Squares and sample-selection models of the demand for medical care. Journal of Business and Economic Statistics 5: 499-506, > 1987 Hays RD, Wells KB, Sherboume CD, Rogers W, Spritzer K. Functioning and well being outcomes of patients with depression compared with chronic general medical illness. Archive of General Psychiatry 52: 11-19, 1995 Heckman JJ. Treatment selection as a specification error. Econometrica 47(1): 153- 161,1979 Heckman JJ, Smith J. Assessing the case for social experiments. Journal of Economic Perspectives 9(2); 85-110, 1995 Hylan TR, Crown WH, Meneades L, Heiligenstein JH, Melfi CA, Croghan TW. Buesching DP. Tricyclic antidepressant and selective serotonin reuptake inhibitors antidepressant selection and health care costs in the naturalistic setting: a multivariate analysis. Journal of Affective Disorders. 47(1-3): 71-79, 1998 Kessler RC, McGonagle KA Zhao S, Nelson CB, Hughes M, Eshleman S, Wittchen HU, Kendler KS. Lifetime and 12-month prevalence of DSM-HI-R psychiatric disorders in the United States. Results from the National Comorbidity Survey. Archives of General Psychiatry. 51(1):8-19,1994 Kozma CM Reeder CE Lingle EW. Expanding Medicaid drug formulary coverage: effects on utilization of related services. Medical Care 28(10): 963-977, 1990 101 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Jollis JG, Ancukiewicz M, DeLong ER, Pryor DB, Muhlbaier LH, Mark DB. Discordance of databases designed for claims payment versus clinical information systems. Annals of Intern Medicine 119(8):844-850,1993 Lee LF. Generalized econometric models with treatment selection. Econometrica 51(2): 507-512, 1983 Lee LF. The computation of opportunity costs in polychotomous choice models with treatment selection. Review of Economics and Statistics 77(3): 421-435,1995 Le Pen C, Levy E, Ravily V, Beuzen IN, Meurgey F. The cost of treatment dropout in depression. A cost-benefit analysis of fluoxetine vs. tricyclics. Journal Affective Disorders 31: 1-18, 1994 Little R. A note about models for treatment selection bias. Econometrica 53(6): 1469-1474,1985 Maddala GS. Limited dependent and qualitative variables in econometrics. ■ Cambridge University Press (NY), 1983 Maddala GS. A survey of the literature on treatment selection bias as it pertains to health care markets. Econometric Methods and Applications II: 331-345, 1990 Manning WG. The logged dependent variable, heteroscedasticity, and the retransformation problem. Journal of Health Economics 17: 283-295, 1998 Martin BC, McMillan JA. The impact of implementing a more restrictive prescription limit on Medicaid recipients: effects on cost, therapy, and out-of-pocket expeditures. Medical Care 34(7): 686-701, 1996 McCombs IS, Nichol MB, Stimmel GL, Sclar DA, Beasley CM Jr, Gross LS. The cost of antidepressant drug therapy failure: a study of antidepressant use patterns in a Medicaid population. Journal of Clinical Psychiatry. 51(suppl 6): 60- 69,1990 McCombs JS, Nichol MB, Stimmel GL. The role of SSRI antidepressants for treating depressed patients in the California Medicaid (Medi-Cal) program. Value in Health 2(4): 269-280, 1999 McCombs JS, Shi L, Stimmel GL. Formulary expansion and the treatment of major depression in the California Medicaid (Medi-Cal) program (manuscript), 2001 102 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. McFarland BH. Cost-effectiveness considerations for managed care systems: Treating depression in primary care. American Journal of Medicine. 97(6 A): 47S-58S, 1994 Montgomery SA, Henry J, McDonald G. Dinan T, Lader M, Hindmarch I, Clare A, Nutt D. Selective serotonin reuptake inhibitors: meta-analysis of discontinuation rate. International Clinical Psychopharmacology 9(1): 47-53, 1994 Moore WJ, Newman RJ. US Medicaid drug formularies: Do they work? Pharmacoeconomics l(suppl 1): 28-31, 1992 Moore WJ, Newman RJ. Drug formulary restrictions as a cost-containment policy in Medicaid programs. Journal of Law Economics 36: 79-97, 1993 Munnane RJ, Newstead S Olsen RJ. Comparing public and private schools: the puzzling role of treatment selection bias. Journal of Business & Economic Statistics 3(1): 23-35,1983 Myers JK, Weissman MM, Tischler GL et al. Six-month prevalence of psychiatric disorders in three communities. Archive of General Psychiatry 41: 959-967, 1984 Preskom SH. Comparison of the tolerability of bupropion, fluoxetine, imipramine, nefazodone, paroxetine, sertraline and venlafaxine. Journal of Clinical Psychiatry 56(suppl 6): 12-21,1995 Regier DA, Hirschfeld RMA, Goodwin FK, Burke JD Jr, Lazar JB, Judd LL. The NIMH Depression Awareness, Recognition, and Treatment Program: structure, aims, and scientific basis. American Journal of Psychiatry 145: 1351-1357, 1988 Rosenbaum PR. Discussing hidden bias in observational studies. Annals of Intern Medical 115: 901-905,1991 Russell JM, Bemdt ER, Miceli R et al. Course and cost of treatment for depression with fluoxetine, paroxetine, and sertraline. American Journal of Managed Care. 5: 597-606,1999 Saklad SR. Pharmacoeconomic issues in the treatment of depression. Pharmacotherapy 15:76S-83S, 1995 SAS Institute, Inc. S AS/ST AT User’s Guide, SAS version 6.12 Cary (NC): SAS Institute, Inc. 1996 103 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Schaffner JA. Generating conditional expectations from models with treatment selection bias: comment. Economics Letters 58: 255-261, 1998 Sclar DA, Robison LM, Skaer TL. Legg RF, Nemec NL, Galin RS, Hughes TE, Buesching DP. Antidepressant pharmcotherapy: economic outcomes in a health maintenance organization. Clinical Therapeutics 16: 715-730,1994 Sclar DA Robison LM, Skaer TL. Galin RS. Trends in the prescribing of antidepressant pharmacotherapy: office-based visits, 1990-1995. Clinical Therapeutics 20: 871-884,1998 Simon GE, Von Korff M, Barlow W. Health care costs of primary care patients with recognized depression. Archive of General Psychiatry 52:850-856,1995a Simon GE, Wagner E, Von Korff M. Cost-effectiveness comparisons using “real world” randomized trials: the case of new antidepressant drugs. Journal of Clinical Epidemiology 48(3): 363-373, 1995b Skaer TL, Sclar DA et al. Economic valuation of amitriptyline, despramine, nortriptyline and sertraline in management of patients with depression. Current Therapeutic Research. 56: 556-567,1995 Smalley WE, Griffin MR, Fought RL, Sullivan L, Ray WA. Effect of a prior- authorization requirement on the use of nonsteroidal antiinflammatory drugs by Medicaid patients. New England Journal of Medicine. 332(24): 1612-1617, 1995 Soumerai SB, Avom D, Ross-Degnan D, Gortmaker S. Payment restriction for prescription drugs under Medicaid: effects on therapy, cost, and equity. New England Journal of Medicine 317: 550-556,1987 Soumerai SB, Ross-Degnan D, Avom J, McLaughlin Tj, Choodnovskiy I. Effects of Medicaid drug-payment limits on admission to hospitals and nursing homes. New England Journal of Medicine. 325(15): 1072-1077, 1991 Soumerai SB. McLaughlin TJ. Ross-Degnan D. Casteris CS. Bollini P. Effects of a limit on Medicaid drug-reimbursement benefits on the use of psychotropic agents and acute mental health services by patients with schizophrenia. New England Journal of Medicine. 331(10):650-655,1994 Streja DA, Hui RL, Streja E, McCombs. Selection contracting and patient outcomes: a case study of formulary restrictions for selective serotonin reuptake inhibitor antidepressants. American Journal of Managed Care 5(9): 1133-1142, 1999 104 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Sturm R, Wells KB. How can care for depression become more cost-effective? JAMA 273(1): 51-58, 1995 Vella F. Generating conditional expectations from models with treatment selection bias. Economics Letter 28(1): 97-103, 1988 Vella F. Estimating models with treatment selection bias: a survey. The Journal of Human Resources 33(1): 127-169,1997 Verbosky LA, Franco KN, Zrull JP. The relationship between depression and length of stay in the general hospital patient. Journal of Clinical Psychiatry 54(5): 177-181, 1993 Viverberg WPM. Educational investments and returns for women and men in Cote d’Ivoire. The Journal of Human Resources 28(4): 933-974,1993 Viverberg WPM. Double selection criteria with multiple alternatives: migration, work status, and wage. International Economic Review 36(1): 159-185, 1995 t Wells KB, Stewart A, Hays RD, Bumam MA, Rogers W, Daniels M, Berry S, Greenfield S, Ware J. The functioning and well-being of depressed patients: results from the medical outcomes study. JAMA 262:914-919,1989 White H. A heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica 48: 817-38, 1980 Zung WW, Broadhead WE, Roth ME. Prevalence of depressive symptoms in primary care. Journal of Family Practice. 37(4):337-44, 1993 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Appendix Adjusting the Standard Errors in the Double Lambda Log Cost Model Section 2.C.3 outlined the estimation methods to correct for the treatment selection bias resulting from dual selection process with multiple alternatives. The appendix aims to provide the procedure to adjust the standard errors of the cost model for the use of two-stage estimation. The formula illustrated here were originally developed for modeling impacts of both the choice of migration and choice of occupations on gender difference in return to education (Viverberg, 1993). First, Equation (2.C.18) defined the disturbance terms for fluoxetine users. It is very easy to extend to any drug group by decision nodes (M, R): (A.l) Vir =lnClr-E[lnClfH ln m< A V ifi< AM In this estimation strategy, normalized distribution equivalents An rn and Anj as well as correlation coefficient p between two stages of choice process were derived based on a standardized bivariate normal density function < t> (A " rii, Ani, p) and cumulative density function < D (A n rn, Ani, p). Therefore the variance of disturbance term can be shown as (A.2) Var(vlr)= o ^ u - e ^ A ^ hn-®i2 A \ h h f - < K A n ni, An x , p )/# (A nrii, An x , p) [(2erll01 -p(0rll2 +e1 2 )] Because the formula for calculating lambda terms in Equation (2.C.16) and Equation (2.C. 17) indicated double lambda terms (X rii and A ,i) must always be R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. negative, researchers need modify the signs of two terms 0r ii2A n r n Adi and 0 i2A niAi when applying Equation (A.2). The Var(Vir) can be estimated from the disturbance terms Vir according to standard formulae proposed by Heckman in his original work (Heckman, 1979). The log health care cost associated with antidepressant r can be rewrite as (A.3) ln[C ir lT jn rii <An r u,rini< A ni]= X ir Pir +|3ir dD +0rn Aru+0iAi+Vir +0rll 8(A*i)+0i8(Ai) In Equation (A.3), the S(Aru) and 8(Ai) is the error of estimated two adjustment terms as t A (A .4) < ^ (^ V |1) = A ril — A rll A (A.5) 8 ( X l ) = X x - \ The implication of Equation (A.3) requires an additional source of variation for the compound disturbance and correlation across observations. As a result, the asymptotic covariance matrix for correcting the standard error in second stage cost is (A.6) V=(X*’X*)'1 X’(Var(vlr)+GrVar(r)G,)X*(X*’X*)'1 In Equation (A.6), X* is a matrix (Xjr A hi A O and F represents all the parameters of the first-stage selection model. G is expressed as the extremely cumbersome derivatives as (A.7) G=9(0rilA r |1 +01 A1 )/a r ’ The formulas to calculate the derivatives G were illustrated explicitly in Viverberg’s paper (Viverberg 1993). 107 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.

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Asset Metadata

Creator Shi, Lizheng (author)

Core Title Effects of a formulary expansion of the use of SSRIs and health care services by depressed patients in the California Medicaid program

School Graduate School

Degree Doctor of Philosophy

Degree Program Pharmaceutical Economics and Policy

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag economics, general,health sciences, health care management,Health Sciences, Pharmacy,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor McCombs, Jeffrey S. (committee chair), [illegible] (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-109276

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

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