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Time dependent survival analysis of Kaiser Permanente/USC pharmacists' consultation intervention study

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Time dependent survival analysis of Kaiser Permanente/USC pharmacists' consultation intervention study

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Content TIME DEPENDENT SURVIVAL ANALYSIS OF KAISER PERMANENTE/USC PHARMACISTS’ CONSULTATION INTERVENTION STUDY by Yong Yuan 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] August 1998 Copyright 1998 Yong Yuan R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 3110963 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3110963 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest 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 S O U T H E R N CALIFORNIA THE G RADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90007 Tnis dissertation, w ritten by YAVâ y i/A /tZ under the direction o f h.(S........ Dissertation Committee, and a p p ro ved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of re quirements for the degree of I or Graduate Studies / U . - D ate August 18, 1998 DISSERTATION COMMITTEE Chairperson .... // / j f / / R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Dedication This dissertation is dedicated to Xiaofeng Lin R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Acknowledgements I was lucky to be a student and research assistant under my advisor, Professor Joel W. Hay. He initiated my interest in pharmacoeconomics and survival analysis. I have benefited greatly from his insights and suggestions that have contributed significantly to the success and improvement of this dissertation. 1 am also indebted to Professor Jeffrey McCombs. Eveiy single discussion with him always resulted in fruitful improvement. His role as leading investigator of the Kaiser project has proved to be extremely valuable to the study. I am thankful to Dr. Susan Groshen for agreeing to be on my committee; and her rich experience in survival analysis has been crucial to the study. Her marvelous ideas lead to a new level of survival analysis with time-dependent covariates structures. Thanks are also due to Joseph Parker for his timely data preparation and many insightful discussions. His wonderful understanding of Kaiser data is invaluable for the study. I would like especially expressing my gratitude for his tremendous efforts in correcting my English spelling and syntax. Ill R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. I would like to extend my gratitude to Professors Gordon Liu, Horland Sather, and Marisue Cody for much valuable input and comments, and also for providing me with relevant papers. At the top of the list of persons 1 am indebted to, is my wife Xiaofeng Lin. With her understanding and consideration, my study was less stressful and more successful. IV R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TABLE OF CONTENTS D edication ii A cknow ledgem ents iii List o f Tables v ii Abstract ix CHAPTER 1 Introduction 1 2 Kaiser P erm anente/USC P atient 10 C onsultation Study 2.1 Background 10 2.2 Pharm acist Consultation Study Design 13 2.3 Pharmacist Consultation Models 15 2.3.1 The Kaiser Permanent Model 15 2.3.2 The State Model 16 2.3.3 The Control Model 16 2.4 Pharmacist Consultation Study Results 17 2.4.1 M^or Findings 17 2.4.2 Limitations 18 3 Survival A nalysis Review 20 3.1 Need / Importance 20 3.2 Challenges 21 3.3 Survival Regression Analysis 23 3.3.1 Overview 23 3.3.2 Cox Proportional Hazards Model 25 3.3.3 Partial Likelihood Estimation 26 3.4 Extension of Cox Proportional Model 30 3.3.4 Time-Dependent Covariates Structure 30 3.3.5 Model Mathematics 31 4 M ethod 32 4.1 D ata 32 4.2 Statistical Model 40 4.3 Full Models vs. Restrictive Model Analysis 41 4.4 Subgroup Analysis 42 4.5 Sensitivity Analysis 44 5 R esults 47 5.1 Survival Analysis Result - Death Eîvent 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.1.1 Descriptive Statistics Results 47 5.1.2 Model Based on Full Set of Variables 50 5.1.3 Model Based on Subset Variables 54 5.2 Survival Analysis Result - Hospitalization Event 55 5.2.1 Descriptive Statistics Results 55 5.2.2 Model Based on Full Set of Variables 55 5.2.3 Model Based on Subset of Variables 58 5.3 Event Elasticity of Alternative Pharmacy Models 59 5.4 Comparison of Time-fixed Model and Time- 61 dependent Cox Model 5.5 Comparison of “Intent to Treat* Model and “As Treated" 63 Time-dependent Cox Model 6 S en sitivity A nalysis 65 7 D iscussion 68 R eference 72 VI R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. LIST OF TABLES Table 1 : Time Dependent and Baseline Covariates Used in the Model 76 Table 2: Description of Death/Hospitalization Events in the Analysis 78 Table 3 : Estimated Risk Ratios for Time-dependent Variables and 79 Baseline Covariates in Total Sample (Death Event) Table 4: Results of Survival Impacts of Alternative Pharmacist 80 Models in Subgroup Analysis (Full vs. Restricted Model) Table 5: 95% Confidence Intervals for Estimated Survival Impacts over 2-year 81 Demonstration Period Table 6; Estimated Risk Ratios for Time-dependent Variables and 82 Baseline Covariates in Total Sample (First Hospitalization) Table 7: Results of Hospitalization Impacts of Alternative 83 Pharmacist Models in Subgroup Analysis (Full Model vs. Restricted Model) Table 8: 95% Confidence Intervals for Estimated Hospitalization Impacts over 84 2-year Demonstration Period Table 9: Estimated Death/Hospitalization Elasticity of Alternative Pharmacy 85 Models in Subgroup Analysis (Time-dependent Cox Full model) Table 10: Results of Model Specification with Time-fixed and Time-dependent 86 Intervention Variables (Death Event) Table 11 : Results of Model Specification with Time-fixed and Time-dependent 87 Intervention Variables (Urgent/Emergency Admission) Table 12: Results of Time-dependent “As Treated” Cox model and “Intent to 88 Treated” Cox Model (Death Event) Table 13: Results of Time-dependent “As Treated” Cox model and “Intent to Treated” Cox Model (Urgent/Emergency Admission) 89 Table 14: Results of Time-dependent Models with Informative 90 Censoring Assumption (Event: Death) Vll R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 15: Frequency of Urgent/Emergency Admission during 2 Year 91 Demonstration Period Table 16: Results of Second Hospitalization Impacts of Alternative 92 Pharmacist Models in Subgroup Analysis (Full Model) Table 17 : The Switching Pattern in the Kmser PermanentAJSC Pharmacists’ 93 Consultation Intervention Study Chart I: Percentage of New Prescriptions Filled at Alternative Pharmacy 94 Models during Demonstration Period Chart H: Survival Impacts of Alternative Pharmacy Intervention 95 Models By Risk Groups Chart ni: Hospitalization Impacts of Alternative Pharmacy 96 Intervention Model by Risk Groups (Urgent/Emergency Admission) V lll R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Abstract Objective: Data from a randomized cohort study are used to evaluate whether pharm acist consultation (PC) interventions have a favorable impact on patient survival and hospitalization. Methods: In the randomized intervention sites, about 80% of the patients switched between the alternative treatm ent models of consultation after initial randomization. Because of this switching behavior, the estimated effect of intervention may be significantly attenuated with a traditional “Intent to Treat* analysis. Similarly, time-fixed “As Treated* analysis may also produce biased results because of the use of future information to predict immediate events. A Cox proportional hazards model was specified that included multiple time-dependent intervention variables and other covariates to better predict the effect of pharmacy interventions on the event rate. Specifically, the num ber of new prescriptions filled over time at each alternative pharm acist consultation intervention site was introduced as the intervention variable in order to measure the extent to which the patient was exposed to each model of pharm acist consultation at any point in time. Separate survival analyses were performed on population subgroups defined according to the level of chronic medication used during the baseline period. Sensitivity analyses IX R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. were done under the assumption of informative censoring. Results: The KP model pharm acist consultation which focused increased resources on high-risk patients significantly reduced the mortality rate relative to both alternative pharmaceutical care treatm ents (State and Control models). The KP model was also found to decrease the likelihood of a urgent/emergency hospital admission in a high-risk group of patients relative to consultation provided only upon patient request or judgem ent of the pharmacist. The State model which mandated consultation for all new or changed prescription was not found to be associated with a risk reduction relative to the Control model, but it decreased the likelihood of death event or a hospital admission relative to the KP model in the Low Risk subgroup. Sensitivity and subset analyses consistently supported these findings. Conclusion: Focusing more resource intensive consultation on high-risk patients may be a cost-effective way of providing pharm acist consultation in the outpatient pharmacy setting. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 1 Introduction Several factors, such as the aging of the population, new technologic advances in medicine, health care cost containment initiatives, and the growth of managed care programs, are at work within the U.S. health care system to provide increasing opportunities for pharm acists in the outpatient setting to positively affect patient outcomes (McCombs et al. 1998). Increased provision of pharmaceutical care for patients in outpatient settings provides a unique opportunity to improve patient outcomes such as quality of life and patient satisfaction. On the other hand, changes in the practice of community pharmacy are constrained by increasing num bers of patients covered by heath insurance plans and government programs which do not recognize value or pay for these cognitive services because of cost concerns. Under these circumstances, the quantitative determination of a positive relationship between pharm aceutical services provided a t a reasonable cost, a n d im proved patient outcomes, becomes an important factor in the justification of an expanded role for the pharmacist. However, existing research R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. quantifying the value of pharm acist consultation in term s of improved patient outcomes and lower costs is veiy limited. Increased pharm acist consultation services might be an effective way to combat drug-related morbidity and mortality and to resolve the problems that threaten a patient’ s adherence to a medication regimen. Drug-related morbidity and mortality are significant problems in the United States. A meta-analysis of 39 prospective studies found that adverse drug reactions may be the fourth-ranking cause of death in the United States, after heart disease, cancer, and stroke. Even if the lower confidence limit of 76,000 fatalities was used, ADRs could still constitute the sixth leading cause of death in the United States (Mean: 106,000, 95% Cl: 76,000-137,000) (Lazarou et al 1998). Many drugs can harm as well as heal. These num bers are veiy conservative because the definition of ADRs excluded therapeutic failures, overdose, and drug abuse. It also did not include adverse events due to errors in drug adm inistration or noncompliance. These figures don’ t mean that it is time to throw out the prescription bottles, but the risks could be reduced substantially if we put as m uch effort into reducing adverse drug reactions as we do into improving highway safely. A recent study reported that drug-related morbidity and mortality resulting from suboptimal medication use may cost the United States an estimated $76.6 billion annually, and that most of the costs associated with inappropriate mediation use may be preventable (Johnson and Bootman 1995). Medication nonadherence R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. may be responsible for almost 10% of all hospital admissions and 23% of all nursing home admissions (Berg JS, et al. 1993). Estimates of the economic costs of noncompliance am ount to approximately 20 million lost working days per year. In addition, there are approximately 140 million prescriptions that remain unfilled per year (McCaffrey et al. 1995). As a result, the role of the pharm acist in the outpatient setting is changing from the traditional role of dispensing product to providing pharmaceutical care and services to all participants in the drug-use process. The redirection of pharmacy profession's role was highlighted by several laws passed in the United States requiring pharm acists to provide consultation to patients. The Omnibus Reconciliation Act (1990) requires a pharm acist's consultation for Medicaid patients when dispensing the medication. In addition, several states, including California, have implemented mandatory patient counseling laws (Nichol and Michael 1992). In California pharmacy practice laws were instituted in November of 1992 which required pharm acists to counsel patients with new or changed prescriptions without regards to the type of medication dispensed or the individual characteristics of the patient. A com prehensive scientific evaluation of the im pacts of the pharm acist consultation services on patient outcomes and costs becomes critical, because mandatory consultation for every new or changed prescription is costly. Health insurance plans and government programs R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. are reluctant to fully implement pharmaceutical care services for all ambulatory patients without reliable data on the effect of these services on health care costs and patient outcome. In addition, the shifting of risk from payer to provider in the HMO environment has placed physicians and other health care providers under increasing pressure to provide only those medical services that optimize patient outcomes in the most cost-effective manner. These challenges, mostly due to economic concerns, become unavoidable and somehow intimidating to current pharmacy practice. However, there is little scientific evidence about the impact pharm acists have on the whole picture of patient outcomes and overall costs. Most existing studies emphasize the ability of the pharm acist to provide more services but do not quantify the value of pharm acist consultation in term s of the impact on patient or drug therapy outcomes (Johnson et al. 1995). In order to provide these answers based on the real data, the Kaiser Permanente Medical Care Program of the Southern California region and the University of Southern California (USC) School of Pharmacy have jointly designed and implemented a study to determine the cost effectiveness of three different models of providing pharm acist consultation (PC) to outpatients. The full study design was described in details in papers by Johnson et al. (1995) and McCombs et al (1995). The State model of pharmaceutical care (State Model) reflects the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. changes in California pharmacy practice laws instituted in November of 1992 which required pharm acists to counsel patients with new or changed prescriptions without regard to the type of medication dispensed or the individual characteristics of the patient. The Kaiser Permanente model of pharmaceutical care (KP Model) focused on patients to whom selected medications were prescribed, these medications are documented in the medical literature to be related with more serious illnesses which place the patient at risk for more serious adverse outcomes if drug therapy is not optimized. Both the State and KP models of pharmaceutical care are compared to a Control Model in which pharm acists practiced under the pre-1992 pharmacy regulations which required consultations only when the patient requested consultation or the pharm acist determined that consultation or other actions were necessary. The results of the pharm acist consultation study regarding satisfaction with pharmacy services, the use and cost of health care services consumed, and the quality of life have been reported by Johnson et al. (1998), McCombs et al. (1998), and Cody et al. (1998) respectively. However, patient migration between treatm ent arm s was a consistent problem in the random assignment arm of the study. At these sites, fewer than 20% of participants assigned to the KP or Control model used their model of pharm acist’ s consultations exclusively for two years. This is because randomly assigned patients could either fill new prescriptions R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. at an after-hours or off-site State Model pharmacy rather than used their assigned pharmacy during normal clinical hours. This switching behavior has created many hurdles in statistical modeling of patient outcomes to accurately evaluate the true impacts of pharm acist consultation intervention. In previous studies, in order to measure the extent to which randomly assigned patients were exposed to each model of pharmaceutical care, the total num ber of new prescriptions filled at KP and State model pharmacies was used to measure the actual treatm ent exposure. Obviously, with a significant problem of low compliance in the study, this use of an “As Treated* model is more appealing when compared to the “Intent to Treat" model. However, other biases may also have been produced in these analyses by using a time-fixed covariate structure developed from the relation between outcomes of interest and patient exposure to the intervention summed over the entire period. Usage of the total num ber of new prescriptions filled during the whole study period to predict outcome events that occurs during the period introduces potential bias. This misspecification of treatm ent variables might have substantial impacts on the study results. The variation due to potential cross-over effects and time effects of these mixed pharm acist consultation interventions by using time-fixed model would be extremely difficult to be separated from the variation from true R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. intervention effects. Advanced statistical techniques need to be developed to get more precise estimations. This paper is devoted to evaluating whether pharm acist consultation intervention models have a favorable impact on two time- related outcomes: patient survival and time to first hospitalization. A survival model was developed and implemented in this study which employed time-dependent covariates due to patient cross-over between treatm ents to minimize potential modeling problems. These time- dependent models can improve model prediction by connecting the outcome event with the actual treatm ent exposure at the time of the event that the more current patients’ treatm ent exposure is more predictive of the event. In addition, our review of the literature shows clearly that previous research made no attem pt to evaluate the survival impacts of pharm acist’ s consultation models. Hawkins et al (1979) reported deaths in their experimental outpatient pharmaceutical services group and in the control group. However, no statistical analysis was conducted in this study to compare the difference in survival. This study will be the first research attem pt to examine these impacts. This dissertation is organized as follows: C hapter two reviews th e history and design of the Kaiser Permanente/USC pharm acists’ consultation intervention study. Major findings and existing modeling limitations in previous studies are described. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter Three presents the need and importance of the time- dependent survival analysis in the pharmacist consultation study. The study challenges invoked by patient switching between alternative models of consultation are emphasized. Time-dependent survival models and their Partial Likelihood Estimation (FLE) method are reviewed. Chapter Four presents a time-dependent survival model structure for analyzing the survival and hospitalization impacts of the pharmacist consultation intervention models. A time-varying covariate structure is used to specify the functional form of the models. Our analysis departs from previous work in th at the intervention variables are specified as time-dependent rather than time-fixed, and the dynamic cumulative current num ber of new prescription is calculated instead of the static total num ber of new prescriptions filled in each pharmacy model over the entire study period. Data and methodological issues in the analyses are described in detail in this chapter. Chapter Five evaluates the intervention impacts of alternative pham acists’ intervention models by using the time-dependent “As- Treated" model. Survival analyses are also performed separately for several patient risk subgroups using both full model specification and restricted model specification. Chapter Six evaluates the sensitivity of our conclusions for the survival impacts of alternative pharmacy consultation models under the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. assum ption of informative censoring in order to test the robustness of conclusions drawn from the survival modeling. Chapter Seven discusses the conclusions and insights from the survival analysis of patient deaths and time to first hospitalization. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 2 The Kaiser Permanente/USC Patient Consultation Study 2.1 Background Pharmaceutical care was defined by Hepler and Strand (1990) as: “...responsible provision of drug therapy for the purpose of achieving definite outcomes that improve a patient’ s quality of life.* Since Federal law requires that pharm acist consultation be provided to patients purchasing prescriptions under the Medicaid program, many states including California have implemented mandatory patient counseling laws. McCombs et al. (1998) argued that, regulatory m andates and legislation could not sustain the full implementation of pharmaceutical care in the outpatient setting. HMO programs may be reluctant to provide direct reimbursement to community pharm acists for cognitive services or increase dispensing fees sufficiently to pay for these services without reliable data on the effects of these services on health care costs an d p atien t outcom es. However, actu al d a ta available to show the significant positive impacts of this pharm acist consultation on patient or drug therapy outcomes are veiy limited. 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Hatoum and Arkras (1993) reviewed 170 articles which reported on pharmacy professional services in ambulatory care settings. However, most of these 170 studies focused on the ability of the pharm acist to provide more services but do not quantify the true impacts of these services in improving the patient outcomes, and none measured survival impacts and quality of life outcomes. Due to obvious limitations in study designs or serious methodological problems in statistical analysis, Hatoum and Arkras concluded that none of these studies can be relied on to evaluate pharmaceutical care intervention models. Several more recent studies suggest that pharmaceutical care may be cost effective if focused on high-risk patients. Munroe et al (1997) evaluated the economic impact of pharm acist intervention in the community retail setting in patients with hypertension, diabetes, asthm a, and hypercholesterolemia. After controlling for age, comorbid condition, and disease severity, the monthly total health care cost was significantly lower in the intervention group relative to the Control group ($723 vs. $ 1,016, p=0.024). Hanlon et al. (1996) evaluated the effect of sustained clinical pharm acist’ s intervention involving elderly outpatients with polypharmacy. They found that pharm acists’ intervention for elderly o u tp atien ts w ith 5 or m ore regularly scheduled m edications h a d no effect on quality of life and patient satisfaction, but inappropriate prescribing significantly decreased. Panley et al (1995) evaluated the impacts of a comprehensive program of asthm a management delivered by a 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. pharm acist and a physician on the num ber of emergency departm ent (ED) visits for acute asthm a exacerbation, and the pharmacist-managed intensive outpatient program was found to reduce ED visits. Patients served as their own control in the study. Sczupak and Conrad (1977) concluded that patient-oriented pharmaceutical services may have a beneficial effect on the outcomes (hospital admissions, medial contacts and compliance) for am bulatoiy diabetes mellitus patients. Although all these studies are also not sufficient to derive a cost-effectiveness conclusion for pharmaceutical care, they strongly suggest that focused pharm acist’ s consultation might be a more economically efficient model for optimizing patient outcomes. There are some precedents in current medical practice for focusing health care resources on specific problematic areas (The Joint Commission 1994; McKenney 1978; Brown 1979; Canada 1976). Focused pharmacy interventions have also been implemented. The Minnesota Medicaid program targeted selected high-risk drugs and patient groups in their Drug Utilization Review program (Kusserow 1989). A large institution in Ohio selected seven drug classes for which consultation would be mandatory. The program in Ohio chose to focus its resources on m edications th a t carry th e greatest risk of adverse effects and that may have the worst consequences if not taken as directed (Koecheler et al. 1989). Unfortunately, little has been reported 12 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. on the overall impacts of targeted pharm acists’ direct patient interventions from these programs. 2 .2 Pharm acist C onsultation Study Design The Kaiser Permanente/USC Patients Consultation Study was initiated in November, 1992 and was fully operational by April 1, 1993. The demonstration project ran for a total of 23 months and entered a phase- down period beginning March 1, 1995. Over 100 Kaiser Permanente outpatient pharmacies took part in the demonstration project, 40 of which required waivers from the California State Board of Pharmacy. Twenty pharmacies continued to practice in accordance with the pharmacy practice regulations that were in place prior to the implementation of mandatory consultations in November of 1992. Twenty additional pharmacies were converted to a Kaiser Permanente Model of pharmaceutical care that focused more pharmaceutical care resources on fewer, “high risk* patients (Johnson et al 1995). The research project consisted of two separate demonstration designs. In the “Random Assignment* design, over 6,000 Kaiser Permanente members were randomly assigned to one of the three models of pharmaceutical care. Seventy-five percent of the randomly assigned patients completed the full two years of the demonstration. The parallel areawide design converted all pharmacies within 6 large geographic sites 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. to a single model of care. Survey data were collected for nearly 4,600 patients residing in these sites. Nearly 63% of patients in this survey sample completed the final survey (McCombs et al. 1998). In all, 20 pharmacies were assigned to deliver the KP model of pharm acist consultations (3 in the random assignment sites, 17 in the geographic implementation sites). Another 20 pharmacies continued to provide services consistent with customary practice prior to mandatory consultation (Control model). All of the remaining 67 pharmacies implemented the new State regulation (State model), including those pharmacies in the three random assignment areas, but no included in the triple sites (McCombs et al 1995). Three years of drug prescriptions (including a baseline period consisting of calendar year 1992 and a two-year period of the demonstration), hospital and outpatient visitation data were retrieved from Kaiser Permanente data systems. Drug prescription data made possible the creation of time-dependent intervention exposure variables that were calculated, on a daily basis, of the cumulative num ber of new prescriptions filled in a given model. 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 .3 . Pharm acist C onsultation (PC) Models 2 .3 .1 The Kaiser Perm anent Model The KP model provided pharm acists’ consultation for high-risk patients who were using selected “high risk* drugs or more than five medications concurrently. The criteria for determining high-risk patients and the list of target drugs were described elsewhere (Johnson et al 1995). The KP intervention model was designed to: 1) be suitable for the outpatient HMO pharmacy practice setting; 2) use the same personnel resources required to implement patient consultation laws m andated by the state of California (State Model); 3) target high-risk patients; and 4) target problems for which pharm acists can make a difference in the outpatient setting. Pharmacists in the KP model were trained to identify and remedy patient medication problems prospectively and take a proactive role for each patient filling a prescription for any of the target drugs, or five or more concurrent medications. At prescription refill, compliance and adverse drug reactions were monitored, and patient questions were answered. It was unclear from available data how much time on an average a pharm acist had actually spent in the KP model of consultation, however, Johnson et al (1995) described how the KP model provides more intensive clinical pharmacy services in outpatient settings. 15 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.3.2 State Model The state of California implemented mandatory patient consultation on November 1, 1992. This law required that pharm acists counsel all patients receiving new or changed prescriptions on the directions for use, storage requirements, relevant warnings and precautions, and the importance of compliance. The State Model here conforms to the requirement mandated by this patient consultation law. Compared with the KP model of pharmacy, the level of intensity of the State model is less than that in the KP model of pharmacy, however, the State model provides many more consultations. 2.3.3 Control Model This model preserved the traditional pharmacy services where the pharm acist provided patient consultation as deemed necessary in his or her professional judgement or upon a request from the patient. The pharmacies in this model were not provided any additional personal resources and thus could not implement counseling beyond those traditionally provided. The maintenance of a control pharmacy model provides the baseline for comparison for the patient outcomes gained under mandatory consultation (State model) and the targeted approach(KP model). The California State Board of Pharmacy provided a 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. waiver of the mandatory counseling requirement for the purposes of the research project to the control and KP model pharmacies. 2.4 Pharmacist Consultation Study Results 2 .4 .1 Major Findings Due to the complex nature of the study design and significant crossover between the alternative models of consultation, the choice of an appropriate statistical model is extremely important. In the study of the use and costs of health services for pharm acist consultation study, a logistic regression model was implemented in the analysis to predict hospital admissions. To control for switching behavior, the treatm ent variables were specified as the total num ber of new prescriptions filled in each model during the 2-year demonstration period. McCombs et al. (1998) found that the KP model decreased the likelihood of a hospital admission over the two-year demonstration period, especially for emergency/urgent admissions. Compared to the Control model, the risk of an urgent or emergency admission was reduced by 4.0%(OR=0.960,p<0.01) for per additional new prescription filled in the KP model. The State model was associated with a smaller impact on urgent/ emergency admissions in the total population than the 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. KP model: 1.3%(OR=0.987,P<0.05) vs. 4.0% relative to Control. This difference between the KP and State models is also statistically significant. Only this KP model of consultation significantly decreased the likelihood of a urgent/emergency admission for some high-risk patients. The State model was not associated with a statistically significant risk reduction in high-risk patients for an urgency/emergency admission. For the study of patient satisfaction outcomes, Johnson et al (1998) found that the non-focused State Model showed higher patient satisfaction than the more focused Kaiser Permanente (KP) model, though differences narrowed with increasing level of patient risk. Satisfaction with waiting time in the pharmacy was not affected by either model of pharm acist consultation. For the quality of life outcomes, pharm acist’ s consultations were not found to affect patient physical or emotional function or overall quality of life (Cody et al 1998). 2.4.2 Limitations However, the use of logistic model does not make full use of the available data to model the time course of an event. Outcome may be best classified in terms of the time to an event, rather than simply the presence or absence of an event over a specified period. In addition. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 18 simple exclusion of censored observations from the data set would largely limit the am ount of data available for analysis and this could lead to significant biases in event prediction. Another obvious problem in using total new prescription counts is of the use of future information to predict intermediate events. The use of num ber of new prescriptions each patient filled at the KP and State model pharmacies during follow-up period as a measure of treatm ent variables introduced biases by using future information to estimate the outcome. Brown et al (1979) have found in a extensive Monte Carlo experiment that usage, as a independent variable, of a covariate that has been calculated over a patient’ s entire follow-up time could lead to severe biases. Therefore, the conclusions from the earlier analyses of hospital admission m ust be re-evaluated using more advanced statistical techniques. In the next chapter, we explore a new way of re-examining these pharm acist consultation intervention impacts using a time- dependent Cox model. In addition, we also consider for the first time the mortality data available in the study. 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 3 Survival Analysis Review 3.1 Need/Importance Survival analysis is extremely useful for studying many different kinds of events; e.g. the onset of disease, death, stock m arket crashes, strikes, arrests, marriages, etc. Because these methods have been applied in different fields, they also go by several different names: Duration Analysis (Economics), Survival Analysis (Biostatistics), Event History Analysis (Sociology), and Reliability Analysis or Failure Time Analysis (Engineering). However, although the name varies, the same technique is applied (Allison 1995). Survival analysis has advantages over conventional statistical methods for analyzing event data for three reasons. First, survival analysis includes the event time information. Conventional logit/probit models analyze data using only a dichotomous dependent variable: event or no event. However, we have good reason to believe that people who die late within a two-year intervention are statistically different from people who die within ju st one week. At minimum, ignoring the time to event information should reduce the precision of the estimates. Second, 2 0 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. survival analysis handles censored data more efficiently. If only a small proportion of people withdraws during the follow-up period, conventional methods work well by discarding the censored cases. However, if withdrawals are not small in number, ignoring the censoring data will result in biased estimates of treatm ent effects. Third, conventional methods employ time-fixed covariates very well. However, if an independent variable varies over time, i.e. the variable is time-dependent, the conventional methods may lead to biased results because they do not take this time-varying factor into consideration. This time variation is particularly problematic if (1) the time-dependent variable is the treatm ent or intervention variable, as it is in this case due to the switching behavior of randomly assigned patients; (2) the event (hospitalization) causes the patient to alter their drug therapy pattern. 3.2 Challenges Survival analysis is a useful approach to estimate the effects of alternative models of pharm acists’ consultation. However, due to the complex nature of the study design and significant cross-over between th e alternative m odels of consultation, several challenges in m odeling survival analysis m ust be overcome. First, in the analysis of time to event data, we often compare treatm ents in terms of the ratio of hazard functions or relative risk (RR). These comparisons determine whether 2 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the risk of an event (such as death) is statistically higher for one treatm ent than the alternative; however, in some settings, patients are first assigned to an initial treatment, but later on they might switch to the other treatm ent for various reasons during follow-up. If the switching rate is low enough, then the “Intent to Treat* analysis usually results in only a small downwards bias of the estimates. However, if the compliance rate is too low, in other words, if many subjects switched during the follow-up period, then the magnitude of the bias may be large. In this situation, consideration of the timing of the treatm ents that patients actually received may be informative. Second, survival analysis can easily yield conclusions that are inaccurate if the model specification is wrong. A common source of error in analyzing the longitudinal data arises from using future information to predict current outcome. Since the event rate at time t after entry is an outcome, its value can depend only on information from the past, relative to time t, and not on information from the future. As time passes on, there is typically more past information that has been compiled for each participant that can be used to estimate the event rate at that time. The process of data analysis m ust assure that future information is not used to define criteria for entry into the study, that future information is not used to estimate the event rate, and that only appropriate data from the past are used for certain types of inference (Wolfe and Strawderman 1996). A previous study using simulated data has shown that we should 2 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. never use a covariate that has been averaged by a patient's entire follow- up time as a baseline covariate, instead, the cumulative exposure up to each point in time should be used as a time-dependent covariate (Brown et al 1979). 3.3 Survival Regression Models 3.3.1 Overview Analysis of the length of time until failure has interested engineers for decades. Likewise, the analysis of survival times, for example, the length of survival after the diagnosis of a disease or after an operation such as a heart transplant, has long been a staple of biomedical research. Social scientists have applied the same body of techniques to strike duration, length of unemployment spells, and so on. The analysis of duration data has recently become more visible in the economics literature. What distinguishes survival analysis from other fields of statistics is censoring. Censoring is an unavoidable and pervasive problem in the analysis of survival data. Random censoring might arise in medical applications w ith anim al or clinical trials. In clinical trials, th e p atien t may decide to move elsewhere - Loss to follow-up; or a patient may discontinue the therapy because of its side effects - Drop out; or there may be Termination of the study. We assum e and require that the 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. random censoring be non-informative; otherwise few results would be available. This assumption seems justified with randomly occurring losses to follow-up. However, if the reason for dropping out is related to the course of the therapy, there may well be informative censoring. Very few methods exist to handle informative censoring. Administrative censoring is another most common censoring in clinical trial. For example, some participants who never had an event (death or hospitalization) when followed up for two years in this study are treated as censored at the end of the study. The administrative censoring is well handled in the survival model and it dose not violate the requirement that censoring should be non-informative in the analysis of survival data. In the conventional regression model that characterizes the conditional mean and variance of a distribution, the regressors can be taken as fixed characteristics at the point in time, or for the individual for which the measurement is taken. When measuring time to event, the observation is implicitly on a process that has been under way for a length of time, which may have changed during the interval. This is a very important factor that we would like to account for in the survival model. However, the treatm ent of time-varying covariates is considerably complicated (Peterson 1986, Green Second Edition). The statistical issues of time-dependent Cox model will be reviewed and explained in details in the next several sections. 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Parametric survival analysis has been less widely applied than the nonparametric regression analysis known as Cox proportional hazards model for a long time. In the following sections, we are only going to review those non-parametric survival techniques. This, however, does not mean that parametric regression analysis is obsolete. If the underlying distribution assumption of the random disturbance term is known, the parametric regression analysis is still more efficient than the nonparametric model. 3.3.2 Cox Proportional Hazards Model Cox (1972) introduced a statistical survival model based on longitudinal data that makes it possible to investigate the impact of each independent variable on the hazard function, adjusted for the confounding influence of the other independent variables. The hazard in the proportional hazards model (sometimes called the Cox model) is defined as the probability of an event at time t, given survival up to time t, and for a specific value of a prognostic variable x. The Cox model is usually written as Mti) = M ti)e-P’ X i [1.1] The function X o(ti) is the baseline hazard. In principle, this is a param eter for each observation that m ust be estimated. Cox introduced a Partial Likelihood Estimator (PLE) which provides a method of 25 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. estimating p without requiring estimation of X o(ti). The estimator is somewhat similar to Chamberlain’ s estimator for the logit model with panel data in that a conditioning operation is used to remove the heterogeneity (Green, Second Edition). If we take the ratio of the hazards for two individuals i and j and apply equation [1.1], then we get; Xi(t)/A,j(t) = exp{pi(X ii - Xji)+ ... + Pk(Xik- Xjk)} The Xo(t) cancels out of the num erator and denominator. As a result, the ratio of the hazards is constant over time. If we graph the log hazards for any two individuals, the proportional hazards property implies that the hazard functions should be strictly parallel. Constructed in this way, the constant term will also be cancelled out of the proportional hazards model (Allison 1995). 3.3.3 Partial Likelihood Estimation Cox argues that the PLE method contains most of the information about P for regression with censored data and that we can ignore the baseline hazard function. In other words, in a partial likelihood estimator, you can estimate the P coefficients of the proportional hazards model without having to specify the baseline hazard function Xo(t). Assume that the first product of the PLE depends on both Xo(ti) and p, and the second product depends of p alone. What partial likelihood does, in effect, is 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. discard the first product and treat the second product - the partial likelihood function - as though it were an ordinary likelihood function. You can get estim ates by finding values of P that maximize the partial likelihood. Since there is some information about ( 3 in the discarded portion of the likelihood function, the resulting estimates are not fully efficient. Their standard errors are larger than they would be if the entire likelihood function were used to obtain the estimates. Efron (1977) and Oakes (1977) have compared the Fisher information in the partial likelihood to the Fisher information in the full likelihood for a variety of models. Usually the information in a partial likelihood (depending on the second product) has a very high efficiency > 90%, and in rare cases, it even carries as much information as the full likelihood. However, what you gain in return by using the partial likelihood method is robustness because the estim ates have good properties regardless of the actual shape of the baseline hazard function. Cox (1972) asserted that partial likelihood estim ates are still asymptotically normally distributed. Tsiatis (1981) gives proof of the asymptotic normality of estimated P using integral representations and stochastic processes which are similar to the proof given by Breslow and Crowley of the asymptotic normality of the partial likelihood estimator and the proof given by Crowley for the Mantel-Haenszel statistic (Miller 1981). To be specific, partial likelihood estimates still have standard properties of ML estimates; they are consistent and asymptotically 27 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. normal. In other words, in large samples, they are approximately unbiased, and their sampling distribution is approximately normal. Another interesting property of partial likelihood estimate is that they depend only on the ranks of the event times, not their numerical values. This implies that any monotonie transformation of the event times will leave the coefficient estimates unchanged. For example, we could add a constant to everyone’ s event time, multiply the result by a constant, take the logarithm, and then take the square root - all without producing the slightest change in the coefficients. An ordinary likelihood function is typically written as a product of the likelihood for all the individuals in the sample. On the other hand, you can write the partial likelihood as a product of the likelihood for all the events that are observed. Thus, if J is the num ber of events, we can write (Allison 1995) J PL ~ Y \L j where L, is the likelihood for the jth event. y=i Assume there are N patients, j people died during trial (tl<t2<t3-— — ), then ^(<i) _ Zj - ________ 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ____________£ A ) _________________________________________________________ ' + + A o (/^ )e ® '“ + ...+ Each time, we delete from the denominator the hazards for all those who have already had events. Also deleted from the denominator are those who have been censored at an earlier point in time. These particular settings in the partial likelihood estimations are attributable to the fact that people under these circumstances are no longer at risk of a defined event. Therefore, we can see that the partial likelihood depends only on the order of the event times, not on their exact values. The censor code is still working since it is used to distinguish the uncensored people from censored people. A general expression for the partial likelihood for data with fixed covariates from a proportional hazards model is as follows: „ g A T , ;= i where Y, =1 if tj>ti| and Y y = 0 if tj<ti. ( The Ys are ju st a convenient mechanism for excluding from the denominator those individuals who already experienced the event and are, therefore, not part of the risk set). Although this expression has the product taken over all individuals rather than all events, the terms corresponding to censored observations are effectively excluded because 5i= 0 for those cases. Once the partial 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. likelihood is constructed, you can maximize it with respect to p ju st like an ordinary likelihood function. However, the formula for the partial likelihood in equation [ 1.2] is valid only for data in which no two events occur at the same time. There are actually some tied event times in this study, so we need an alternative formula to handle those situations. The most plausible method is the Exact or Efron method. It is reasonable to suppose that ties are merely the result of imprecise measurement of time and that there is a true time ordering for any event that occurred in a time point. If we knew that ordering, we could construct the partial likelihood in the usual way. In the absence of any knowledge of that ordering, however, we have to consider all the possibilities of ordering (Allison 1995). 3 .4 E xten sion o f Cox Proportional M odel 3.4.1 Time-Dependent Covariates Structure Time-dependent covariates are those that may change in value over the course of observation. To modify the model in equation [1.1] to include tim e-dependent covariates, we need to w rite (t) after th e Xs th a t are tim e dependent. For a model with one fixed covariate and one time-dependent covariate, we have Log A .i(t) = log X o(t) + PiXii + B2Xi2(t) 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Xii are time-fixed variables, such as baseline value of sex or race variables Xi2 (t) are time-dependent variables which are allowed for changing values of some variables. 3.4.2 Model Mathematics With time-dependent covariates, the partial likelihood function has the same form we saw previously in equation [1.2]. The only thing that changes is that the covariates are now indexed by time. PL-Y{[----------1 1 = 1 ;= i The estimation of the P coefficients in the presence of time- dependent covariates is more computationally intensive because the values of Xj (b) are changing as a function of ti 31 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 4 Methodology 4.1 Data The data come from the Kaiser Permanente/USC Patient Consultation Study during a baseline period of calendar year 1992 and a 23-month demonstration period (April 1, 1993, February 28, 1995). A parallel, prospective study was designated to evaluate the impacts of the State and KP models of pharmaceutical care on patient outcomes and costs relative to Control. The current survival analysis considers the same 6,063 participants who were randomly assigned to three different practice models in the original report of the study design. A more detailed description of the original study design can be found in Johnson et al. (1995) and McCombs et al. (1995). The Areawide sample in which geographic areas were converted to a single model of pharmacy was not included in this study for two reasons. First, the extraneous events (i.e., January 1994 Northridge Earthquake) and other factors such as changes in physician staffing at the regional Kaiser Permanente hospitals may be highly correlated with geographic site. These correlation will confound the true intervention survival impacts. We can not remove these extra sources of variation 32 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. from our models based on the available information, however, ignoring them will bias our estimation of true intervention effects. Fortunately, these biases might be avoided by using data from the randomized arm of the study because these three pharm acist consultation models are located at 3 geographic sites and should have been equally affected by these unexpected events. Second, the geographic implementation of the three pharm acist models has minimized the likelihood of patient cross over between models, and using time-varying *As Treated* in this arm of the study was unnecessary. An “Intent to Treat* model, which is beyond the interest of this paper, might be more appropriate for the analysis in the Areawide data. Our end points of interest in this study are death and first hospitalization events. There are 5,499(90.7%) patients included for survival analysis in the Triple site sample. All participants included in the statistical analyses had to have filled at least one new prescription during the two-year demonstration period. Included participants had to have relatively complete baseline survey data for all the independent variable in the statistical analysis. The imputation of missing values for a limited num ber of survey responses was undertaken to m aintain sample size (McCombs et al. 1998). Due to the lack of information about the causes of death, deaths from all causes were analyzed. For example, deaths due to heart failure or cancer could be treated the same as deaths due to accidents. Death 33 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. information was derived from three sources: 1. Kaiser Records; 2. Defined Death Certificates; 3. Family Reports. Those patients for whom information on date of death was unavailable were assigned death event times by using the dates when they were last seen in either the pharmacy or clinic. This rough approximation might somewhat underestimate the death event times; however, the systematic bias will be greatly minimized by using partial likelihood estimation, because the partial likelihood technique is only concerned with the ranks of the event time. Furthermore, there is no reason to suspect that this information is correlated with the patient’ s exposure to the alternative model of pharmaceutical care. In addition, patients alive at the end of 2-year demonstration period were treated as censored. Time to first hospitalization event was analyzed for urgent/ emergency type admission. Clearly, it is not reasonable to treat all types of hospital admissions as equivalent events. If the KP model of pharmaceutical care is effective in reducing hospital admissions during the 2-year demonstration period, the intervention effects are most likely to be observed in emergency/urgent admissions. In this study, we treated participants who did not have hospitalization event at the end of demonstration period as censored. 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Specification of the Intervention Variables In the pharmacist consultation intervention site, about 80% of the participants filled at least one new prescription in pharmacies other than the pharmacy to which they were originally assigned. Patients had the option of filling new prescriptions at an after-hours State model pharmacy for acute episodes of illness or at off-site model pharmacies, possibly after visits to specialists at other sites. As a result, treatm ent selection bias was a potentially severe problem in the study. For example, participants with poorer health status may be more prone to use the after hour or off-site State model pharmacies near specialists practice site. The results of an “Intent to Treat* analysis may be then made up of a mixture of the true treatm ent effect plus the effects confounded with effects due to health status differences. Therefore, we need a strategy that simultaneously takes account of the intervention actually received and controls for various confounding factors. The total num ber of new prescriptions filled at a given model of pharmacy was introduced in the previous studies as the intervention variable in order to m easure the extent to which patients were exposed to each model of pharmaceutical care over the 2-year demonstration period. However, o th er biases m ight have been produced in these analyses by u sin g a time-fixed covariate structure developed from the relation between outcomes of interest and patient characteristics at ju st one fixed time the end of the follow-up period. It might not be appropriate to use such 35 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. model on follow-up data to obtain updated prediction, especially for these treatm ent variables, at least, the estimated intervention effects are not very precise. By using the above definition of the intervention variable, the time- fixed “As Treated” analysis employs future information to predict the current outcome. In such settings, we considered the Cox model for inference about the relative risk by using a multiple time-dependent covariates structure to specify a continuous functional form for the relative hazard as a function of time since the switch. The intervention variables were redefined as the cumulative num ber of new prescriptions filled at a given model pharmacy for a given event day to predict the event rate. It is time-consuming to calculate the values of time- dependent variables for each event time, particularly for hospitalization events, therefore, the values of these intervention variables were measured in days, and for each day during the demonstration period, we constructed a variable indicating the cumulative num ber of new prescription filled at different pharmacy models from computerized prescription data. Specification of Other Time-dependent Variables Table 1 shows the definitions of two other time-dependent variables in the analyses. The after-hour pharmacy use in the random assignment 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. sites for new prescriptions was created as a time-dependent covariate to capture a potential measurement of severity of illness. After-hours pharmacy use for new prescriptions may be positively correlated with the acuity and severity of the illness treated. All after-hours pharmacies in the random assignment sites provided the State model of care. We suspect that acutely patients were more likely to use after-hours pharmacies and if so, the State model pharmacy would contain more acutely ill patients, therefore, simply assigning these after-hours new prescriptions to the State model would confound the true treatm ent effect, or more precisely, overestimate the risk of the State model. To control for these confounding severity of illness effects, for each day during the demonstration period, a time-dependent variable was created to reflect the ratio of cumulative after-hours pharmacy use for filling new prescriptions to the total of new prescription filled. In the analysis of first urgent/ emergency hospitalization event, one additional time-dependent dichotomous variable - elective admission was created to reflect whether patients have a history of elective hospital admissions. We suspect that whether a patient has a prior elective admission might be somehow correlated with subsequent urgent/emergency admission, and this might also confound the true impacts of pharm acist consultation models. 37 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Specification of baseline covariates The significant switching problem in the study has contaminated the randomized design. Baseline covariates were needed to enter the multivariate statistic models in order to control for differences in patient characteristics across the three pharmacy models to remove extra sources of variation and to improve param eter estimation precision. These baseline covariates could also influence both the pattern of treatm ent changes and the risk of events. In this case, controlling for them could reduce the bias in the “As Treated* analyses. For example, if it so happened that sicker patients were more likely to change from the Control to the State model, then the current State model pharmacy would contain sicker patients, and so its risk would be overestimated unless proxies for health status or severity of illness are included in the model. The computer-based data and survey data from pharm acist consultation study created a wealth of information about the enrollees’ demographic and health status characteristics at baseline. In order to be consistent with the previous pharm acist consultation study analyses, we used the same set of explanatory variables (McCombs et al 1998). The description of these baseline covariates included in this study is shown in Table 1. Prior utilization of health services at baseline period was used to create num ber of prior hospital admissions and outpatient visit 38 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. variables. Two dummy variables (CPLYHIO and CPLYMEDO, see table 1) were created to control for the difference in medication compliance behavior at the baseline based on a Morisky scales (Morisky et al 1986). Survey responses from eight SF-36 scales were converted into normalized t-scores to capture patient health status at baseline (Hays et al 1993). Variables for pain, mental, physical function, emotional role function, physical role function, social function, vitality and general health were developed. Higher score means better health status in general. Imputation for measuring data in any one of these eight domains of health status were based on statistical models which regressed each dimension of health status on the remaining seven dimensions and other patient characteristics. An error term was added to the imputed value which reflected the variation in the study population for the missing data. Patients with two or more missing values for SF-36 health status dimension at the baseline period were dropped from all analyses (McCombs et al 1998). Prescription drug data from the year prior to the dem onstrated project (1992) were used to create 28 dichotomous variables detailing the mix of drug classes used by the patient prior to the study period. In order to control for difference in demographic and socieconomic characteristics, age, race, education, marital status, and employment status were also used in the model. Smoking and drinking variables 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. were used to control for health behavior differences in the analysis. Data on income were not used due to a significant num ber of missing values. A five-level variable reporting the patient’ s trend in health status (much better to much worse) was also used to create a set of 5 dichotomous variables for the patient’ s general health trend. Survey respondents who failed to answer this item were coded as having no change in health which served as the comparison category. 4.2 Statistical Models The time-dependent Cox model is specified as following: Log Mt) = log Xo(t) + % + yiKKPi (t)+ yaSSTi (t)+ ya TTTi (t)+ y 4 RatiOi (t) + y g Elect, (t) where t = event time Log X ,i(t) - the logarithm of the hazard function for an individual i log X o(t) - the logarithm of baseline hazard P - a. vector of coefficients of baseline covariates X f - a vector of baseline covariates y (yl y2 y3 y4 y5) - coefficients of time-dependent covariates KKP (t) - the cumulative num ber of new RXs filled in the KP model 40 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. at time t SST (t) - the cumulative num ber of new RXs filled in the State model at time t TTT (t) - the cumulative num ber of new RXs filled in all three models at time t Ratio (t) - the ratio of the cumulative num ber of new RXs filled in after- hours pharmacy to the total num ber of new RXs filled at time t Elect (t) - whether patients had a prior elective admission for an urgent/emergency admission. This variable is only used in the analysis of hospitalization event. The SAS PHREG procedure was used to perform the Cox Proportional Hazards model with a time-dependent covariate structure. To deal with large num ber of events which occur on the same day (ties) in this study, the Efron method was used in partial likelihood estimation since it is relatively less time-consuming than the Exact method. 4.3 Full Model vs. Restricted Model Analysis We presented two sets of m odels. The first m odel (Full model) w as based on full set of the variables included in the published time-fixed logistic models (McCombs et al. 1998) with substitutions for time-dependent variables for the num ber of new prescriptions filled at a specific 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. pharmacy model, ratio of after-hours pharmacy use, and prior elective admission in the analysis of first hospitalization event. The Restricted model consists of only those variables found to be statistically significant baseline variables by using a backward Cox regression model (P=0,1 was the level of entiy and removal of covariates in the backward regression). Time-dependent variables were forced to enter this regression model as a sensitivity analysis. We wanted to see whether usage of various subsets of independent variables has significant impacts on estimated param eters for the treatm ent variables. 4.4 Subgroup Analysis Since the three alternative intervention models focused on different target populations, intervention effects were expected to be sensitive to the population being studied. Thus, subsets of population were designated for sub-analysis in the study. The subgroups are: 1. The Polypharmacy and Target Medication Population. This population was defined as patients who filled at least a new prescription for a target medication and used five or more chronic medications during the baseline period. This subgroup of p atien ts w as supposed to receive services under both State and KP model, but was expected to show more significant effects from the KP model of care due to its relative intensity of pharmaceutical care. 42 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2. The Target-only Population. This population consists of patients who filled a new prescription for one or more of the medications targeted for intervention in the KP model, but who did not fill five or more new prescriptions for chronic medications during the baseline period. This group was also expected to show more significant effects from the KP model of care. 3. The Low Risk Population. This population consisted of patients who filled at least one prescription but did not use any target medication or take 5 or more chronic medications during the baseline period. It is expected that the impact of the KP model of care will be minimal within this risk class of patients due to the low likelihood that these patients received any pharmaceutical intervention in the KP pharmacy. However, the State model pharmacy should have some impacts on these patients due to their having filled at least one new prescription. 4. The High Risk Drug Population. This subgroup focuses in on patients who filled prescriptions for some high-risk medications during the baseline period. These high-risk medications consist of NSAIDS, or drugs for anxiety, COPD, diabetes, epilepsy and seizure disorders. 43 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5. The Failing Health Population. The final sub-population consists of patients who reported their health status at baseline as “worse* or “much worse* than the previous year. 4.5 Sensitivity Analysis Although the survival techniques should handle censored data very well, partial likelihood estimation requires that random censoring be noninformative. Some patients in this study dropped out during the 2- year period, and these observations are censored. Unfortunately, it is not hard to suspect that those who drop out might be among those most likely to experience an event if they stayed until completion, or alternatively that they wouldn’ t have an event until after the end of the study. Informative censoring can lead to severe biases in principle, but it is difficult in this situation to gauge the magnitude or direction of those biases. There is no statistical test for informative censoring versus noninformative censoring. You can compare the performance records and personal characteristics of those who dropped out and those who stayed, but these are generally factors that would be included as covariates. Therefore, the prim ary concern is w hat m ight be called residual informativeness, after the effects of covariates have been taken into account. The best that can be done by way of correction is to 44 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. include any factors that are believed to affect both event times and censoring times. In this study, sensitivity analysis of informative censoring was performed to test the robustness of the results. In conducting the sensitivity analysis, two differing assum ptions will be made. The first is that censored observations experience events immediately after they have been censored. This corresponds to the hypothesis that censored cases are those that tend to be at high risk for an event. The opposite assum ption is that censored cases have longer times to events than anyone else in the sample. This corresponds to the hypothesis that censored cases are those at lowest risk for an event. Then we can see how sensitive these estimates are to possible informative censoring. The results and conclusions will be more robust if treating death as noninformative censoring has no appreciable effect on the conclusions. In addition, all the models in the previous analyses have focused on the intervention impacts of alternative pharmacy models on the first event of interest. These analyses are sufficient for death events. However, there are many repeated hospitalization events that are also of interest to us. Therefore, we are going to apply the same time-dependent survival analysis to the second urgent/emergency admission in order to explore whether alternative pharmacy intervention models have the same impacts on the second hospital admission as that of the first admission. In the analysis of the second urgent/ emergency admission, the event 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. time was defined as the time interval between the first urgent/emergency admission and the second urgent/ emergency admissions. The total sample in this analysis was limited to those who had at least a first urgent/emergency admission during 2-year demonstration period. Patients who did not have a second urgent/ emergency admission during 2-year demonstration period were treated as censored. 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 5 Results 5.1 Survival Analysis Result - Death Event 5.1.1 Descriptive Statistics Results The study includes all patients who participated in the Kaiser Permanente/USC Pharm acists’ Intervention study between April 1, 1993 and February 29, 1995. The 5,499 patients who filled at least one new prescription in any of these alternative models during the 2-year follow- up are included in the study. Patients who dropped out from the trial or who were still alive at the end of the study are treated as censored. Table 2 shows the event distribution for various risk groups. Of the 5,499 participants in this study, 83 died during the two-year period (1.51%). Of the 3,102 who used target medications, only 31 died (1.00%); of the 751 who used both more than five drugs or target medications, 39 died (5.19%); of the 1,270 who neither used Polypharmacy or target medications (Low Risk Group), only 12 died (0.94%); there were 28 and 65 death events in respectively Failing Health and High Risk subgroups, the proportion of death events being 3.75% and 1.73%. 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Low compliance due to patients filling new prescriptions at an after-hours or off-site State model pharmacy or electing not to go to their assigned pharmacy during normal clinic hours is obvious. Chart I shows the cumulative percentage of new prescriptions filled at alternative pharmacy models during the demonstration period. At the beginning of the demonstration period, there were about 33.3% participants assigned to each of three alternative pharmacy models. During the first 200 days of the demonstration period, about half of all new prescriptions were filled at State model of consultation. Only approximately 18% and 30% new prescriptions were respectively filled at the KP and Control models of consultations. This decrease in percentage of new prescriptions filled in the KP and Control models of consultation is mainly due to the fact that patients elected to fill new prescriptions at an after-hours or off-site State model pharmacy or electing not to go to their assigned pharmacy during normal clinic hours. The percentage distribution of new prescriptions filled at alternative pharmacy models is pretty consistent over the 2-year period. Table 17 shows that the compliance rate is a decreasing function of time. Those patients who were originally assigned to the State model of pharm aceutical care have relatively higher com pliance rate am ong alternative pharmacy models, 49.1% of these patients were always going to their assigned pharmacy model for the first 200 days, and this num ber drops to 31.9% at the end of the study. During the 2 year 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. demonstration period, 67.0% of those patients who were originally assigned to the State model have filled more than 50% of their new prescriptions at the State model, and about 45.9% of these patients have filled more than 80% of their new prescriptions at the State model. Only a small percentage of patients have most of their new prescriptions filled at the KP or Control model. Those patients who were originally assigned to the Control or KP model of pharmaceutical care have very low compliance rate, only 10.1% of patients in the Control model and 6.4% of patients in the KP model were always going to their assigned pharmacy model during the two-year demonstration period. 36.4% of those patients who were originally assigned to the Control model have filled most of their new prescriptions at the State model, and 34.5% of those who were assigned to the KP model have filled most of their new prescriptions at the State model during the two year period. The compliance data strongly suggest that we need to use a proxy instead of simply the initial assignment to capture the actual treatm ent that patients received. 49 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.1.2 Model Based on Full Set of Variables Effects of KP and State Models Table 3 and Chart II show the estimated relative risk (RR) of mortality for the KP and the State models versus the Control model. The null hypothesis is “ There is no difference in RR between the intervention model and control model.” The estimated treatm ent effects are expressed as relative risk. For example, a relative risk of 0.90 associated with the KP model indicates that, compared to the Reference model of pharmaceutical care, for every additional new prescription filled in the KP model, the risk of an event was reduced by 10%. Over two years, the overall relative risk of any death for the KP intervention model was 0.921 (95% Cl=0.876, 0.970:P=0.002), an average of 7.9% reduction in total mortality (Table 4 and 5). In other words, if the baseline mortality rate is one percent over two years, for every 10,000 enrollees in the Kaiser Permanente plan who have filled one additional new prescription at a KP model pharmacy, about eight patients will be expected to have avoided death over the 2-year period. Approximately 7.8% risk reduction was also found in KP model compared to State model of pharmaceutical care (RR=0.922, 95% CI=0.874, 0.972: P=0.003)(Table 5). This overall significant risk reduction by the KP model of pharmaceutical care may be largely attributable to the tremendous risk reduction found in high-risk subgroups. 50 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Over a 2-year period, a 16.0% risk reduction of death event by the KP intervention model was seen in the Target Medication subgroup (RR = 0.840, 95%CI=0.746, 0.945: P=0.004). A 7.8% risk reduction by the KP model was found in the High Risk Drug subgroup (RR=0.922, 95% CI= 0.869,0.978:P=0.007). A strong statistically significant risk reduction was also found in the KP model compared to the State model of pharmaceutical care in the Target Medication group (RR=0.826, 95%C1=0.725,0.941, P=0.004) and High Risk Drug group (RR=0.922,95%Cl=0.869,0.978;P=0.013)(Table 5). About 7.1% and 9.5% risk reduction by KP model were found in both Polypharmacy + Target Medication subgroup (RR=0.929, 95%CI=0.854,1.011: P=0.848) and Failing Health subgroup (RR=0.902, 95%CI=0.806,1.010, P=0.075). However, these risk reductions were not statistically significant. These results were consistent with our prior expectations that the KP model would have the most pronounced impacts in high-risk subgroups. This finding is very intriguing because, after only two years, under the intervention of KP model pharmacy, a significant mortality reduction has been found in the high-risk population, and this reduction is also statistically significant. It was not too surprising that the KP model of pharmaceutical care was found to be associated with higher risk of mortality (RR= 1.494, 95%CI= 1.144,1.950) relative to the State model in the Low Risk subgroup during 2-year demonstration period. This finding is consistent 51 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. with our expectation that the impact of the KP model of pharmaceutical care would be minimal within this risk class of patients due to the low likelihood that these patients received any intensive pharmaceutical intervention in the KP model pharmacy. The State model should have more pronounced impacts on this group of patients because this group of patients were more likely to receive the State model of pharmaceutical care. However, it was surprising to see that, in the Low Risk subgroup, the KP model was also found to be related with an increase in mortality rate relative to the Control model of pharmaceutical care during 2-year demonstration period. This is probably a statistical fluke because only small num ber of deaths was observed in this subgroup. No significant survival impacts for the State intervention model were found either in the overall population or for any subgroup relative to Control model. We ai e still not sure if the long term survival impacts of the State intervention model will be significant since we only followed patients for two years. Effects of Other Confounding Variables The results for the time-dependent Cox model based on the full set of independent variables in the Total sample are shown in Table 3. As expected, after-hours pharmacy use was associated with an increased 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. likelihood of mortality during the 2-year demonstration period, however this association was not statistically significant (P=0.317). Most of the baseline variables are within our expectation to have meaningful signs and hypothesis testing. Neoplastic or organ transplant patients, older people, male, less educated patients, retired and much worse patients’ general health trend each were associated with a higher mortality rate (P<0.05). Two dummy variables which were used to identify patients who used anti-anxiety or non-steroid anti-inflammatoiy agents were each associated with a lower mortality rate (P<0.05), however, these two variables were excluded from the restricted model because they were not statistically significant at the significance level of 0.1. Latino patients were associated with a lower mortality rate in the Full model (P<0.05), however, this association was not statistically significant in the Restricted model (P<0.05). 5.1.3 Model Based on Subset Variables Effects of KP and State Models The findings from models based on only significant variables are very close to those of the Full models except for the risk reductions for KP model in Failing Heath subgroup and Polypharmacy and Target Medication subgroup now becoming statistically significant (Table 4). 53 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. This further confirms that high-risk patients are more sensitive to the KP intervention model. Effects of Other Confounding Variables The time-dependent Cox model based on only significant regressors is shown in Table 3. These estimated param eters in these analyses are also similar to those in the Full model analyses. By the time-dependent transformation, after-hours pharmacy use was also associated with an increased likelihood of mortality during the 2 year demonstration period (P=0.268). Variables ANXYO, NSAIDYO, SINGLE, HIGHS, HIGHG, COLLS and COLLG became insignificant at the significance level of 0.1 and were removed from the restricted model. 5.2 Survival Analysis Result - Hospitalization Event 5.2.1 Descriptive Statistics Results In the survival analysis with the first urgent/ emergency hospitalization events, patients who were never admitted to the hospital over two years were treated as censored. As shown in Table 2, there were 592 patients with at least one urgent/emergency hospital admissions in the total sample of 5499 patients over two years. The Polypharmcy and Target subgroup has the highest rate of hospital admission; 22.37% of patients 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. in this subgroup were admitted into the hospital over the 2-year demonstration period. The Failing Health, High Risk Drug and the Target groups have the second, third and fourth highest occurrences of hospital admission (14.75%, 13.11% and 10.83%). There are only 4.96% with hospital admissions in the Low Risk Group. 5.2.2 Model Based on Full Set of Variables Effects of KP and State Models The results for urgent/emergency admission events are summarized in and Table 6 and Chart III. Two interesting findings emerge from this part of the analysis. First, only the KP model of pharmaceutical care was found to be associated with a statistically significant risk reduction in some high-risk subgroups. A 5.5% risk reduction was found in the KP model of pharmaceutical care relative to Control model in the Target Medication subgroup (RR=0.945, 95%CI=0.901, 0.992: P=0.021) (Table 7 and 8). In the High Risk Drug subgroup, a 3.3% risk reduction was found in the KP model of pharmaceutical care relative to the Control model (RR=0.967, 95%CI=0.836, 0.999: P=0.045). However, the statistically significant risk reduction was not found for the KP model of pharmaceutical care in the Total sample. Second, the KP model was again found to be associated with higher risk of the first urgent/ emergency admission in the Low Risk 55 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. subgroup relative to State model during the two-year period (RR= 1.301, 95%CI= 1.077, 1.570) (Table 8). This finding is within our prior expectation because patients in this subgroup were not likely to receive any pharmaceutical intervention from the KP model pharmacy but the State model pharmacy should have interacted with these patients due to their having filled a new prescription. It is not surprising that the KP model of pharmaceutical care was found to significantly reduce the likelihood of first urgent/ emergency type hospitalization compared with the Control model in some high-risk subgroups because the KP model used additional resources and provided more pharmaceutical care than the Control model in high-risk group. However, no such favorable impacts have been found for the State model in Total sample and any subgroup. Since the KP model provided more intensive pharmaceutical care to high-risk patients than the State model, we have a good reason to believe that the intensity of pharmaceutical care might play a distinguishing role in favor of the KP model of pharmaceutical care. Because the study only lasted for two years, we need more data to determine whether the State model of consultation has significant impacts on hospital admissions in the long run. In addition, surprisingly, the statistically significant intervention effects on urgent/ emergency admission were not found in the Polypharmacy and Target group in the analysis of both intervention models, especially for the KP model of consultation. One possible 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. explanation is that this subgroup consists of very sick people (taking both target medication and more than five prescription drugs at the same time), these two intervention models especially KP model did not have immediate impacts on urgent/ emergency hospital admission within 2- year period. Another explanation might be due to insufficient power of the study to detect a significant difference in this subgroup. However, we suspect that the impact of the KP model might be significant in the long run or in subsequent hospitalization admissions for this subgroup. Effects of Other Confonnding Variables The estimated param eters of other confounding variables in the time- dependent Cox model for the first urgent/ emergency admission event are shown in Table 6. As expected, by the time-dependent transformation, a prior elective admission was found to be strongly associated with an increased likelihood of the first urgent/emergency type admission during the 2-year demonstration period (P=0.000). As expected, the baseline variables have meaningful coefficient signs. Older people, more frequent hospital admission at the baseline period, lower SF-36 general health perceptions, physical function or social function t score, usage of acid peptic disease agents, black, Indian, retired and smoking were each significantly associated with the higher probability of an urgent admission (P<0.05). The variables BP_TO and Female were each significantly associated with the likelihood of an 57 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. urgent hospital admission (P<0.05), however, they became insignificant at the significance level of 0.1 and were removed from the restricted model. Latino patients were associated with the lower likelihood of an urgent admission, however, it became insignificant in the restricted model. 5.2.3 Model Based on Subset Variables Effects of KP and State Models The findings from models based on only significant variables are consistent with those of full models (Table 7). There are some difference in magnitude of estimated intervention effects, however, these difference are not significant enough to reverse the conclusion drawn from the full models. Effects of Other Confounding Variables The estimated effects of other confounding variables in the time- dependent Cox model based on only significant regressors are shown in Table 6. By the time-dependent transformation, the history of a prior elective admission was still found to be associated with an increased likelihood of first urgent/emergency admission during the 2-year demonstration period. After-hour pharmacy use was also found to increase the likelihood of first urgent/emergency admission (P<0.10). 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Variable Latino in this restricted became insignificant (P>0.10). Estimated effects in the restricted models for other baseline variables are very close to the findings in Full models except for some minor changes in magnitude. 5.3 Ebrent Elasticity of Alternative Pharmacy Models In previous analyses, we presented the results in terms of estimated relative risk. However, what this estimated ratio m easures is the relative risk reduction associated with each additional new prescriptions filled at a model pharmacy. In order to analyze a more meaningful “treatm ent effect* we need to determine the elasticity of death/ hospitalization with respect to changes in treatment. That is to say, we need to answer the question: “How does a percent increase/ reduction in new prescriptions filled at the KP or State models of consultation impact the percent change in death/hospitalization.* This is a unit-free m easurem ent of treatm ent impact. The elasticity is defined as %(change in outcome)/%(change in treatment) or d (logy)/d (logx). Table 9 shows the estimated death/ hospitalization elasticity of alternative pharmacy intervention models. The magnitude of estimated elasticity was shown to be relatively smaller than that of estimated relative risk. In the analysis of death event, the estimated death elasticity is -0.271 for the KP model in the Total sample. This num ber 59 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. suggests that, for every one percent increase in new prescriptions filled at the KP model of consultation relative to the Control model, the mortality rate will be reduced by 0.271% over two year period. Compared with death event analysis, the overall risk elasticity (-0.100) is smaller in the analysis of hospital admission. The treatm ent effects of alternative pharmacy models, which were found to be statistically significant in some high-risk subgroups, were also re-evaluated based on elasticity measurement. For each one percent increase in new prescriptions filled at the KP model of consultation relative to the Control model, 0.534% and 0.322% risk reductions in mortality were separately achieved in Target Medication subgroup and High Risk subgroup. The estimated event elasticity was also smaller in the analysis of hospitalization event in these two high-risk subgroups. The estimated hospitalization elasticity i s -0.180 for Target Medication subgroup and -0.141 for High Risk subgroup. In other words, the KP model of consultation was found to reduce urgent/emergency hospital admissions by 0.180% for the Target Medication subgroup and by 0.141% for the High Risk Drug subgroup for eveiy one percent increase in new prescriptions filled at the KP model relative to the Control model of consultation. 6 0 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.4 Comparison of Time-fixed models and Time-dependent Cox Models The significant difference in the results between the time-fixed and time- dependent models has shown how important and appropriate model is for the analysis. Table 10 shows the estimated risk ratios and p vgdues for death event at the significance level of 0.05. The hazard ratio related to the num ber of new prescriptions filled at an alternative pharmacy model was assum ed to be either 1) fixed in time or 2) could be estimated at different time points by respectively specifying the time-dependent covariates. Note that the estimated relative ratios of the fixed regressors for the KP model of pharmaceutical care (Logistic and Time-fixed Cox model) were not significant at the conventional significance level of a=0.05 in the Total sample and High Risk subgroup; however, they become significant when they were specified as time-dependent covariates. The majority of patients in the High Risk subgroup used target medications or multiple medications, we expected that the KP model would have more pronounced impacts in this high-risk subgroup relative to Control, however, this difference was not found in time-fixed models. Instead, this significant difference in mortality was found in the model with time- dependent specifications. In this analysis, the magnitude of estimated risk ratio for Total sample and each subgroup is very close between time- fixed and time-dependent models. 6 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In the analysis of the first urgent/emergency type hospital admission, the KP model was found both in logistic model and time-fixed Cox model to be associated with lower risk of hospitalization over two year period compared with the Control model in Total sample (?<0.05)(Table 11). However, in the time-dependent analysis, the KP model of consultation was not found to be associated with a risk reduction in the Total sample (P>0.05) but with a significant risk reduction in some high-risk patients (P<0.05). Both findings are within our prior expectation that a significant risk reduction would be found in the KP model of consultation for some high-risk subgroups. In addition, a significant hospitalization risk reduction was found for the Control model of consultation in the Low Risk subgroup compared with the KP model in the logistic regression model and time- fixed model. However, using the time-dependent Cox model, we instead found that no such significant difference in RR was found between the KP and Control models of pharmaceutical care in this subgroup. The finding from time-dependent Cox model is more meaningful because we expected that the KP model would not be different from the Control model in this Low Risk subgroup due to the fact that these patients were not likely to receive any consultation service from the KP model of pharmaceutical care. These direct comparisons between time-fixed and time-dependent models suggest that a proper form of model specification may be crucial 6 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. to forming accurate conclusions in the study. All of above data shows that, of three assum ed model specifications, the time-dependent Cox model is a more attractive model. This model includes all potential confounding variables, and the time transforms for the actual treatm ent change, after-hours pharmacy use, and a prior elective admission. 5.5 Comparison of “Intent to Treat” models and Time-dependent “As Treated” Cox Models Table 12 shows the estimated risk ratios and P values for death event in “Intent to Treat" models and “As Treated" time-dependent Cox models. As of a naïve analysis, the “Intent to Treat" model might be used to provide some information about how much biases have been introduced in this model compared to “ As Treated" Cox time-dependent model. Estimated param eters and hypothesis testing are totally different in these two model specifications. In the analysis of death event, the risk reductions were shown to be much higher for the KP models in the “Intent to Treat" Cox models relative to the “As Treat" time-dependent models in the Total sample and some high-risk subgroups. These huge risk reduction figures are not realistic in this two-year demonstration study. In addition, the hypothesis testing results are also totally different in these two model specifications. Significantly bigger risk reductions were also shown in the analysis of hospitalization admission 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. by using the “Intent to Treat" models (Table 13). These findings are not too surprising to us, since the significant switching behavior has contaminated the randomized design, the results from the “Intent to Treat" analyses are biased. 64 R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Chapter 6 Sensitivity Analysis In order to test whether the alternative assumption of informative censoring has some impact on our previous results, a sensitivity analysis was conducted under two opposite assum ptions of censoring data; one is that censored observations experience events immediately after they are censored (i.e., these patients are at the highest level of risk); the other is that censored cases have longer times to events than anyone else in the sample (i.e., these patients are at low risk of an event). Tables 14 shows the results of sensitivity analysis for death event. There are approximately 7.22% censored cases (don’ t count the administrative censoring) in the study. For death event analysis, we have to clarify one thing before looking at the results. All patients in the study have been coded exclusively to identify if they were either dead or alive during the 2-year period, and this information excludes the possibility that censoring cases might have a death event during the follow-up period. Therefore, assum ing that censored cases are at the highest risk of death is actually unnecessary here. Tables 14 shows that the estimated values of risk ratios are veiy close across various assum ptions of random censoring, and the 65 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. hypothesis testings are as well. The previous results and conclusions are proven to be robust under this analysis. Sensitivity analysis strongly supported the conclusion that the KP model is a favorable intervention model in reducing mortality in high-risk subgroups, and treating death as noninformative censoring has no appreciable effect on the conclusions. Informative censoring was not assum ed in the analysis of hospitalization event, since each included patients in the study has been clearly identified as either having observed hospital admissions or no admission during 2-year demonstration period. Table 15 shows the frequency of urgent/ emergency type hospital admission during 2-year demonstration period. There were 592 patients who had at least one urgent/emergency admission during 2-year demonstration period. The maximum num ber of urgent/emergency admissions is 15. Of 592, there were 420 (70.9%) patients who had only one urgent/emergency admission during 2-year period; there were 86(14.5%) patients who had exactly two urgent/ emergency adm issions in the study. There were 172 patients (29.1%) who had multiple admissions (two or more than two admissions) during 2-year demonstration period. Previous analyses have focused on the impacts of pharmacy intervention on the first urgent admission, however, it does not mean that an analysis of subsequent hospital admissions is not of interest to 6 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. us. Table 16 shows the estimated relative risk of second urgent/emergency admission for the KP and the State models versus Control. Signs of relative ratios suggested that the KP model of pharm acist consultation was associated with a reduced likelihood of patient experiencing a second urgent/emergency admission in the Total sample and each high risk subgroup relative to Control during the 2-year demonstration period, however, these associations were not statistically significant (P>0.05). In addition, the KP model of consultation was found to be associated with a risk reduction in the Total sample relative to the State model (P<0.05). This significant risk reduction found in the Total sample was mainly attributable to a bigger risk reduction for the KP model relative to the State model of consultation in the defined High Risk subgroup (P<0.05). This finding is also within our expectation that the KP model would have more pronounced effect on high-risk patients compared to the State model of pharmaceutical care. The State model was not shown to be associated with a risk reduction in the Total sample or any subgroup relative to the Control. These findings suggested that the intensity of pharmaceutical care might continue to have an important impact on subsequent hospital admissions. 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 7 Discussion We attempted to minimize the treatm ent selection bias created by patient crossover among treatm ents in this study by combining baseline covariates and time-varying treatm ent variables into our analysis. Sensitivity analyses were also run by examining the assum ption that the censoring was informative. Full models and restricted models were separately estimated in the study to check if our results were affected by using a subset of all variables. We found that the findings were very consistent under a variety of different model specifications. Based on the results from time-dependent survival analysis, the KP model was found to be superior to the State and Control models in term s of survival impact in total population and high-risk subgroups. In the analysis of the first urgent/emergency admission event, the KP model was found to have positive impacts on hospital admission over 2-year demonstration period relative to the Control model in some high-risk subgroups. However, in the analysis of both death event and hospitalization event, no such advantage was found in the State model of pharmaceutical care compared with the Control model. Instead, the State model was shown to have a significant risk reduction compared 6 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. with the KP model in both death event and the first urgent/emergency admissions over 2-year period in Low Risk subgroup. The latter finding is not surprising because the State model of consultation used additional resources to provide more consultation services in this subgroup. In light of these results, we concluded that, for high risk population, during the 2-year demonstration period, the KP model of pharmaceutical care was a better pharmacist consultation model among those alternative models of pharmaceutical care. However, no such significant differences were found for the State model in high-risk subgroups. The observed trend for the State model, although compatible with benefit, was not significant at the 0.05 level. We would expect that, with a larger sample, these differences would then become significant. In addition, further study is needed to analyze the long-term impacts of pharmaceutical care models. The provision of more intensive pharm acist consultation services to targeted patients has been shown potentially favorable in improving patient outcomes before. It is not too surprising from the origin of the study design that we derived these favorable results for the KP model in terms of survival in only two years. It is easy to explain why the KP model is better than Control model. The Control model is a traditional way of providing pharmacy services, where the pharm acist provides patient consultation as deemed necessary in his or her professional judgm ent or upon request of the patient. The pharmacies in this model 69 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. were not provided additional resources and could not implement counseling beyond that traditionally provided. Compared with the control model, the KP and States models used more resources and provided more intensive and comprehensive clinical pharmacy services to patients. Johnson et al. (1998) explained that there are three primary differences between the KP and State models. First, the KP model provides more comprehensive services rather than ju st point-of-service consultations. Second, the KP model targets only high-risk patients, as opposed to the State model, which covers all patients. Third, the KP model systematically evaluates the common problems for each high-risk drug, so the pharm acist has a guideline for intervention with high-risk patients. The State model has no drug-specific guidelines for pharm acist consultation or intervention, only topics that should be covered during the consultation. Therefore, it not too surprising that, even if the KP model of outpatient pharmacy practice was designed to use the same level of total organizational resources as the State model, it is still advantageous over both the Control model and the State model in term s of overall survival or urgent/ emergency admission impacts. We should point out here that the intensity level of the pharm acist consultation intervention does play an important role in affecting the patients outcomes within only 2-year period. 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. However, caution m ust be still taken to the fact that the KP model of pharmaceutical care was also found to be associated with a higher risk of mortality and hospitalization in the Low Risk subgroup during 2-year period. Intensive pharmaceutical care for target patients should be balanced to avoid any potentially reduced role of pharmaceutical care towards low-risk group of patients. Our study shows that the selection of an appropriately specified model and the use of detailed information from patients’ actual utilization data are essential to the accurate evaluation of true impacts of an intervention model in this study. Failure to incorporate these factors may lead to seriously flawed conclusions. 71 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. References Allison PD (1995), “Survival Analysis Using the SAS System, A Practical Guide,” SAS Institute, Cary, NC, USA. Berg JS , Dischler J , W agner D J, et al.(1993), “Medication Compliance: A Health Care Problem. Ann Pharm acotherapy. 27(Suppl), S5-S19. Brown D J, Helling DK, Jon es ME (1979), “Evaluation of Clinical Pharm acist Consultation in the Family Practice Office,” Am J Hosp Pharm ., 36, 912-915. C anada AT. (1976), “The Pharm acist and Drug Compliance. In: Sackett DL, Hayne RD, eds. Compliance with Therapeutic Regimens,” Baltimore: Jo h n s Hopkins University Press; 129-134. Carter BL and Helling DK (1992), “Ambulatory Care Pharm acy Services: The Incomplete Agenda,” Annals of Pharm acotherapy, 26, 701-708. Cody M., McCombs J ., et al. (1998), “ The Kaiser P erm anente/USC Patient Consultation Study: Quality of Life Outcome.”(in press). Cox, D.R. (1972), “Regression Models and Life-tables. Jo u rn a l of the Royal Statistical Society,” Series B 34, 187-202. Cox, D.R and Snell, E. J . (1989), “The Analysis of Binary D ata,” Second Edition, London: C hapm an & Hall. Efron, B (1977) “The Efficiency of Cox’ s Likelihood Function for Censored D ata,” Jo u rn al of the American Statistical Association 72, 557-565. Green W.H., Econometric Analysis. Second Edition. 715-727. Hawkins, DW, Fiedler FP, et al. (1979), “Evaluation of a Clinical Pharm acist in Caring for Hypertensive and Diabetic Patients,” Am J Hosp Pharm 36, 1321-1325. Hepler CD, Strand LM. (1990), “O pportunities and Responsibilities in Pharm aceutical Care,” Am J Hosp Pharm , 47, 533-543. 72 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Hays RD, Sherbourne CD, Mazel RM (1993): The RAND 36-item health survey 1.0. Economics, 2, 217-227 Johnson K., McCombs J., et al. (1998), “The Kaiser P erm anente/USC Patient Consultation Study: Patient Satisfaction Outcom es.”(in press). Johnson JA and Bootman JL. (1995), “Drug-related Morbidity and Mortality: A Cost of Illness Model. Arch Intern Med., 155, 1949-1956. Johnson K., Nye M., et al. (1995), “M easuring the im pact of Patient Counseling in the O utpatient Pharm acy Setting: Development and Im plem entation of the Counseling Models for the Kaiser P erm anente/USC Patient Consultation Study,” Clinical Therapeutics, 17, 5, 988-1002. Knowlton CH and Knapp DA (1994), “Community Pharm acists Help HMO C ut Drug Costs,”, American Pharm acy, Ja n u aiy , Vol. NS34, 1, 36- 42. Kusserow RP, (1989), Medicare Drug Utilization Review Program, Office of the Inspector General, Federal D epartm ent of Health and H um an Services. Control #OAI-01-88-00980, Ja n u a iy 1989. Koecheler JA, Abramowitz PW, Swim SE, et al. (1989), “Indicators for the Selection of Ambulatory Patients Who W arrant Pharm acist Monitoring,” AM J Hosp Pharm ., 46, 729-732. Lazarou J , Pom eranz BH and Corey PN (1998), “Incidence of Adverse Drug Reactions in Hospitalized Patients.”, JAMA, April 15, 279, 15., 1200-1205. McCaffrey D J, Sm ith MC, et al.(1995), “The Financial Im plications of Initial Noncompliance: An Investigation of Unclaimed Prescriptions in Community Pharm acies”, Jo u rn al of Research in Pharm aceutical Economics, Vol. 6(1). McCombs J.S ., Cody M., et al.. (1995), “M easuring the Im pact of Patient Counseling in the O utpatient Pharm acy Setting: The Research Design of the Kaiser P erm anente/USC Patient C onsultation Study,” Clinical Therapeutics, 17, 6, 1188-1206. McCombs J., Liu G, et al. (1998), “The Kaiser Perm anente/USC Patient Consultation Study: The Use and Costs of Health Services.”(in press). 73 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. McKenney JA. (1978), “Effect of Pharm acist Drug Monitoring and Patient Education on Hypertensive Patients,” Contemp Pharm Pract. 1, 50- 56. Magee, L. (1990), “R2 M easures Based on Wald and Likelihood Ratio Jo in t Significance Tests,” The American Statistician, 44, 250-253. Miller RG. (1981), “Survival Analysis. Wiley Series in Probability and M athem atical Statistics,” Applied Probability and Statistics, 4-5. Morisky DE, Green LW and Levine DM. C oncurrent and Predictive Validity Of A Self-reported M easure of Medication Adherence. Medical Care, 24(1): 67-74 Munroe WP, Kunz K, Dalmady-Israel C, Potter L, Schonfeld WH. (1997), “Economic Evaluation of Pharm acist Involvement in Disease M anagem ent in a Community Pharm acy Setting,” Clinical Therapeutics, 19(1), 113-123. Nichol MB, Michael L.(1992), “A Critical Analysis of the C ontent and Enforcem ent of M andatory Consultation and Patient Profile Laws,” Ann Pham acother, 26, 1149-1155. Oakes, D. (1977), “The Asymptotic Information in Censored Survival D ata,” Biometrika 64, 441-448. O m nibus Reconciliation Act of 1990 (1990), W ashington, DC. US Government Printing Office. Pauley TR, Magee MJ, and Cury JD (1995), “Pharm acist-M anaged, Physician-Directed Asthm a M anagem ent Program Reduces Emergency D epartm ent Visits.”, The Annals of Pharm acotherapy, Ja n u aiy , Vol. 29, 5, 5-9. Peterson, T. (1986), “Fitting Param etric Survival Models with Time- D ependent Covariates,” Jo u rn al of the Royal Statistical Society, Series C (Applied Statistics), 35, 281-288. Sczupak, CA. and Conrad WF. (1977), “Relationship between Patient- oriented Pharm aceutical Services and Therapeutic Outcom es of Ambulatory Patients with Diabetes Mellitus,” Am J Hosp Pharm , 34, 1238-1242. The Joint Commission on Accreditation of Healthcare Organizations (1994), Accreditation M anual for Hospitals, Chicago, III. 74 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Tsiatis, A. (1981), "A Large Sample Study of Cox’ s Regression Model. Annals of Statistics,” 9, 93-108. Wolfe RA. and Straw derm an RL. (1996), “Logical and Statistical Fallacies in the Use of Cox Regression Models. American Jo u rn a l of Kidney Disease,” 27, NO l(JanuEiry), 124-129. 75 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 1 : Time-dependent and Baseline Covariates Used in the M odel Variable Name Variable Description Code 5 tim e-deoendent covariates KKP Cumulative number of new RXs in KP model # SST Cumulative number of new RXs in State model # ITT Cumulative number of new RXs in all models # RATIO Ratio of after-hours pharmacy use to the total new RXs in all models Otol ELECT Whether a patient has a prior elective admission 1=Yes, 0=No 59 baseline covariates YOVISIT # of outpatient visits in 1992 # ADMO # of admission in 1992 # CPLYHIO High compliance( Ref; Low Compliance) 1=Yes, 0=No CPLYMEDO Medium Compliance (Ref: Low compliance) 1=Yes, 0=No BP TO SF-36 pain index t score Oto 100 GH TO SF-36 general health perceptions t score Oto 100 MH TO SF-36 mental health Index t score Oto 100 PF TO SF-36 physical function t score Oto 100 RE TO SF-36 role-emotlonal t score Oto 100 RP_TO SF-36 role-physical t score Oto 100 SF TO SF-36 social functioning t score Oto 100 VT TO SF-36 pain Index t score Oto 100 ANXYO Antl-anxlety agents 1=Yes, 0=No CFYO Meds for cystic fibrosis 1=Yes, 0=No GOPDYO Meds used In respiratory Inllness&asthma 1=Yes, 0=No CROHNYO Meds used for Crohn's disease&ulcerative colitis 1=Yes, 0=No CVDYO Cardiac medications 1=Yes, 0=No DEPRYO Anti-depressants 1=Yes, 0=No DIABYO Diabetic medications 1=Yes, 0=No EPIYO Anticonvulsants 1=Yes, 0=No GLAUYO Meds for glaucoma 1=Yes, 0=No GOUTYO Meds used for gout 1=Yes, 0=No HTNYO Hypertensive meds 1=Yes, 0=No LIPYO Meds for hypetilpldemia 1=Yes, 0=No LIVRYO Meds for liver failure 1=Yes, 0=No MANOYO Meds used In bipolar disorders 1=Yes, 0=No NEOYO Antl-neoplastic meds 1=Yes, 0=No NSAIDYO Non-steroid antl-lnflammatory meds 1=Yes, 0=No PAINYO Narcotic analgesics 1=Yes, 0=No PRKYO Meds for Parkinson's disease 1=Yes, 0=No PSYCYO Antl-psychotics 1=Yes, 0=No RAYO Meds for rheumatologic conditions 1=Yes, 0=No TBYO Anti-tubercular meds 1=Yes, 0=No 76 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Variable Nam e Variable Description Code B aseline covariatesf Continued) THYYO Thyroid replacement meds 1=Yes, 0=No TRNSYO Meds used with organ transplants 1=Yes, 0=No ULCRYO Meds for acid peptic disease 1=Yes, 0=No FEMALE Female 1=Yes, 0=No SINGLE Single 1=Yes, 0=No SEPER Separated 1=Yes, 0=No WIDOW Widowed 1=Yes, 0=No ASIAN Ethnicity-asian 1=Yes, 0=No BLACK African-American 1=Yes, 0=No INDIAN Ethnicity-indian 1=Yes, 0=No LATINO Ethnicity-hispanic 1=Yes, 0=No HIGHS Some Night School (Ref: grade school) 1=Yes, 0=No HIGHG High school graduate (Ref: grade school) 1=Yes, 0=No COLLS Some college (Ref: grade school) 1=Yes, 0=No COLLG College graduate (Ref: grade school) 1=Yes, 0=No COLLPG Postgraduate degree (Ref: grade school) 1=Yes, 0=No UNEMP Unemployed 1=Yes, 0=No RETIR Retired 1=Yes, 0=No DISAB Disabled 1=Yes, 0=No STHMKER Student or full tme homemaker 1=Yes, 0=No BBETTER SF-36 health transition: much better (Ref: Same) 1=Yes, 0=No BETTER SF-36 health transition:somewhat better (Ref: Same) 1=Yes, 0=No WORSE SF-36 health transition:somewhat worse (Ref: Same) 1=Yes, 0=No WWORSE SF-36 health transition.much worse (Ref: Same) 1=Yes, 0=No SMOK Smoking 1=Yes, 0=No DRINK Drinking 1=Yes, 0=No AGE Age Continuous 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2: D escription o f Death and H ospitalization E vents in th e A nalysis Subgroup N Death Hospitalization* Number Percentage Number Percentage Total Sample 5499 83 1.51% 592 10.77% Target Medication Sample 3102 31 1.00% 336 10.83% Polypharmacy + Target Medication Sample 751 39 5.19% 168 22.37% Failing Health Sample 746 28 3.75% 111 14.75% High Risk Drug Sample 3752 65 1.73% 492 13.11% Low Risk Group Sample 1270 12 0.94% 63 4.96% Hospitalization refers to urgent/em ergency type adm ission 78 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 3: Estimated Risk Ratios for Time-dependent Variables and Baseline Covariates in Total Sample (Death Event) Variable Full Model* Restricted Model** RR P Value RR P Value Time-denendent covariates KKP 0.921 0.002 0.928 0.001 SST 1.000 0.980 0.996 0.803 TTT I.I05 0.000 1.082 0.000 RATIO 1.487 0.317 1.499 0.268 Baseline covariates AGE 1.034 0.021 1.032 0.008 ADMO 1.164 0.194 I.OIO 0.931 BP_TO 1.025 0.091 1.035 0.002 PF T O 0.939 0.000 0.948 0.000 ANXYO 0.428 0.026 ----- NEOYO 2.684 0.003 2.699 0.001 RAYO 1.239 0.487 1.440 0.184 NSAIDYO 0.514 0.016 TRNSYO 11.043 0.009 9.147 0.005 FEMALE 0.524 0.022 0.501 0.005 SINGLE 2.404 0.054 ----- LATINO 0.215 0.027 0.397 0.129 WIDOW 0.515 0.146 0.479 0.073 HIGHS 0.229 0.036 HIGHG 0.314 0.065 COLLS 0.305 0.046 COLLG 0.255 0.035 COLLPG 0.II7 0.004 0.382 0.043 RETIR 2.596 0.018 2.892 0.003 DISAB 1.697 0.287 1.924 0.I3I WWORSE 4.356 0.008 2.175 0.065 * Only significant variables (P<0.10) are listed in this table for the full model wdiich uses full set of regressors in the study. ** Restricted model was derived by running backward regression on all regressors except for time-dependent variables first, and then combining all regressors from the backward regression result with time-dependent variables to get parameter estimations. This variable was not included in the restricted model 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4: Results of Survival Impacts of Alternative Pharmacist Models in Subgroup Analysis (Full model vs. Restricted model) Population Regressors Estimated Risk Ratio and ( P Value) Time-dependent Cox Model (Full Model) Time-dependent Cox Model (Restricted Model) Total Sample KP 0.921(0.002)** 0.928(0.001)** N=5,499 STATE 1.000(0.980) 0.996(0.803) Model Chi-square*** 626.651 547.953 Target Medication KP 0.840(0.004)** 0.889(0.014)* N=3,102 STATE 1.017(0.582) 0.999(0.975) Model Chi-square*** 326.888 286.766 Polypharmacy+Tar- KP 0.929(0.089) 0.927(0.043)* get Medication STATE 0.974(0.442) 0.990(0.748) N=751 Model Chi-square*** 162.905 120.636 Failing Health KP 0.902(0.075) 0.903(0.020)* N=746 STATE 0.938(0.171) 0.956(0.248) Model Chi-square*** 150.363 119.916 High Risk KP 0.922(0.007)** 0.916(0.000)*** N=3,752 STATE 0.996(0.827) 1.001(0.931) Model Chi-square*** 519.129 409.718 Low Risk KP 1.963(0.008)** 1.610(0.000)*** N=l,270 STATE 1.314(0.185) 1.144(0.201) Model Chi-square*** 143.361 141.584 ♦ P<0.05 ** P<0.01 P<0.0001 8 0 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5: 95% Confidence Interval for Estimated Survival Impacts over 2-year Demonstration Period Study Sample Reference Group Control Model RR(95% Cl) State Model RR(95% Cl) Total Sample KP 0.921(0.876, 0.970)** 0.922(0.874, 0.972)** State/Control* 1.000(0.965, 1.035) 1.000(0.966, 1.036) Target Medication KP 0.840(0.746, 0.945)" 0.826(0.725, 0.941)** State/Control 1.017(0.958, 1.079) 0.983(0.927, 1.044) Polypharmacy+Target KP 0.929(0.854, 1.011) 0.954(0.877, 1.038) State/Control 0.974(0.910, 1.042) 1.027(0.960, 1.099) Failing Health KP 0.902(0.806, 1.010) 0.962(0.874, 1.059) State/Control 0.938(0.855, 1.028) 1.066(0.973, 1.169) High Risk Drug KP 0.922(0.869, 0.978)** 0.926(0.870, 0.984)* State/Control 0.996(0.960, 1.033) 1.004(0.968, 1.042) Low Risk Group KP 1.963(1.194, 3.228)** 1.494(1.144, 1.950)** State/Control 1.314(0.877, 1.969) 0.761(0.508, 1.140) 95%CI: 95% Confidence Interval, results are based on the flill model analysis. * P<0.05 ** P<0.01 *** P<0.0001 & State/Control refers to State model if the Control model was defined as reference model; or it refers to Control model if the State model was defined as reference model 8 1 R eproduced with perm ission of the copyright owner. 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Table 6: Estimated Risk Ratios for Time-dependent Variables and Baseline Covariates in Total Sample (First Hospitalization) Variable Full Model* Restricted Model** RR P Value RR P Value Time-denendent Covariates KKP 0.972 0.078 0.973 0.075 SST 0.987 0.347 0.981 0.144 TTT 1.039 0.000 1.039 0.000 RATIO 1.176 0.227 1.263 0.074 ELE 16.324 0.000 13.649 0.000 Baseline Covariates AGE 1.014 0.003 1.010 0.000 ADMO 1.296 0.000 1.326 0.000 BP T O 1.012 0.025 - - - - - - - - - - GH_TO 0.980 0.000 0.979 0.000 PF_TO 0.988 0.014 0.987 0.003 SF T O 0.990 0.025 0.991 0.047 COPYO 1.178 0.111 1.205 0.109 NSAIDYO 1.172 0.078 1.131 0.149 PRKYO 1.913 0.059 2.163 0.019 ULCRYO 1.342 0.007 1.367 0.003 FEMALE 0.754 0.004 BLACK 1.354 0.003 1.379 0.001 INDIAN 2.582 0.010 2.671 0.006 LATINO 0.927 0.010 1.029 0.853 RETIR 1.468 0.004 1.536 0.000 STHMKER 1.176 0.364 1.255 0.168 SMOK 1.313 0.018 1.301 0.017 * Only significant variables (P<0.10) are listed in this table for the full model vriiich uses full set of regressors in die study. ** Restricted model was derived by running backward regression on all regressors except for time-dependent variables first, and then combining all regressors from the backward regression result with time-dependent variables to get parameter estimations. This variable was not included in the restricted model 8 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 7: Results of Hospitalization Impacts of Alternative Pharmacist Models in Subgroup Analysis (Full model vs. Restricted model) Population Regressors Estimated Risk Ratio and ( P Value) Time-dependent Time-dependent Cox Model (Full Model) Cox Model (Restricted Model) Total Sample KP 0.972(0.078) 0.973(0.076) N=5,499 STATE 0.987(0.347) 0.981(0.144) Model Chi-square*** 1964.836 1942.291 Target Medication KP 0.945(0.021)* 0.952(0.032)* N=3,102 STATE 0.990(0.602) 0.989(0.577) Model Chi-square*** 1165.914 1149.172 Polypharmacy+Tar KP 0.966(0.176) 0.989(0.636) get Medication STATE 0.981(0.369) 0.986(0.491) N=751 Model Chi-square*** 291.172 250.111 Failing Health KP 0.969(0.395) 0.978(0.519) N=746 STATE 1.000(0.993) 1.003(0.927) Model Chi-square*** 534.040 499.588 High Risk KP 0.967(0.045)* 0.966(0.032)* N=3,752 STATE 0.980(0.134) 0.976(0.067) Model Chi-square*** 1323.016 1313.108 Low Risk KP 1.113(0.209) 1.128(0.157) N=l,270 STATE 0.856(0.082) 0.889(0.152) Model Chi-square*** 780.837 766.497 * P<0.05 ** P<0.01 *** P<0.0001 83 R eproduced with perm ission of the copyright owner. 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Table 8: 95% Confidence Interval for Estimated Hospitalization Impacts over 2-year Demonstration Period Study Sample Reference Group Control Model RR(95% Cl) State Model RR(95% Cl) Total Sample KP 0.972(0.942, 1.003) 0.984(0.954, 1.015) State/Control* 0.987(0.962, 1.014) 1.013(0.986, 1.040) Target Medication KP 0.945(0.901, 0.992)* 0.955(0.910, 1.002) State/Control 0.990(0.952, 1.029) 1.010(0.972, 1.051) Polypharmacy+Target KP 0.966(0.920, 1.015) 0.985(0.940, 1.032) State/Control 0.981(0.941, 1.023) 1.019(0.978, 1.063) Failing Health KP 0.969(0.902, 1.042) 0.969(0.907, 1.035) State/Control 1.000(0.938, 1.067) 1.000(0.938, 1.066) High Risk Drug KP 0.967(0.836, 0.999)* 0.987(0.956, 1.019) State/Control 0.980(0.954, 1.006) 1.021(0.994, 1.048) Low Risk Group KP 1.113(0.942, 1.315) 1.301(1.077, 1.570)* State/Control 0.856(0.718, 1.020) 1.169(0.980, 1.393) 95%CI: 95% Confidence Interval, results are based on the full model analysis * P<0.05 *♦ P<0.01 *** P<0.0001 & State/Control refers to State model if the Control model was defined as reference model; or it refers to Control model if the State model was defined as reference model 84 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 9: Estimated Death/Hospitalization Elasticity of Alternative Pharmacist Models in Subgroup Analysis (Time-dependent Cox Full Model) Population Regressors Death Event Admission Risk Ratio Elasticity Risk Ratio Elasticity Total Sample KP 0.921** -0.271 0.972 -0.100 N=5,499 STATE 1.000 0.000 0.987 -0.039 Target Medication KP 0.840** -0.534 0.945* -0.180 N=3,102 STATE 1.017 0.058 0.990 -0.032 Polypharmacy+Tar KP 0.929 -0.450 0.966 -0.212 get Medication STATE 0.974 -0.159 0.981 -0.120 N=751 Failing Health KP 0.902 -0.418 0.969 -0.129 N=746 STATE 0.938 -0.269 1.000 0.000 High Risk KP 0.922** -0.322 0.967* -0.141 N=3,752 STATE 0.996 -0.020 0.980 -0.082 Low Risk KP 1.963** 1.791 1.113 0.214 N=l,270 STATE 1.314 0.581 0.856 -0.272 * P<0.05 ** P<0.01 ♦** P<0.0001 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 10: Results of Model Specifications with Time-fixed and Time-dependent Intervention Covariates (Death Event) Estimated Risk Ratio and ( P Value) Population Regressors Time-fîxed Logistic Model Time-fixed Cox Model Time-dependent Cox Model Total Sample N=5,499 KP STATE Model Chi-square*** 0.947(0.074) 1.004(0.851) 438.975 0.953(0.100) 0.998(0.898) 472.778 0.921(0.002)" 1.000(0.980) 626.651 Target Medication N=3,102 KP STATE Model Chi-square*** 0.850(0.033)’ 0.997(0.933) 217.968 0.869(0.036)* 0.995(0.857) 245.556 0.840(0.004)“ 1.017(0.582) 326.888 Polypharmacy+Tar get Medication N=751 KP STATE Model Chi-square*** 0.963(0.439) 1.005(0.885) 113.641 0.969(0.494) 1.001(0.987) 133.722 0.929(0.089) 0.974(0.442) 162.905 Failing Health N=746 KP STATE Model Chi-square*** 0.954(0.447) 0.969(0.486) 96.528 0.962(0.523) 0.983(0.658) 99.368 0.902(0.075) 0.938(0.171) 150.363 High Risk N=3,752 KP STATE Model Chi-square*** 0.939(0.071) 0.995(0.820) 360.999 0,942(0.079) 0.991(0.638) 399.464 0.922(0.007)“ 0.996(0.827) 519.129 Low Risk N=l,270 KP STATE Model Chi-square*** 1.876(0.008)“ 1.420(0.070) 96.756 1.819(0.008)“ 1.383(0.080) 100.510 1.963(0.008)“ 1.314(0.185) 143.361 Results are all based on full model analysis * P<0.05 ** P<0.01 *** P<0.0001 8 6 R eproduced with perm ission of the copyright owner. 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Table 11: Results of Model Specification with Time-fixed and Time-dependent Intervention Covariates (Urgent/Emergency Admission) Estimated Risk Ratio and ( F Value) Population Regressors Time-fîxed Logistic Model Time-fîxed Cox Model Time-dependent Cox Model Total Sample N=5,499 KP STATE Model Chi-square*** 0.973(0.032)* 1.000(0.976) 1087.289 0.978(0.009)** 1.006(0.324) 1403.521 0.972(0.078) 0.987(0.347) 1964.836 Target Medication N=3,102 KP STATE Model Chi-square*** 0.960(0.030)* 0.990(0.479) 568.023 0.968(0.011)* 1.011(0.162) 754.377 0.945(0.021)* 0.990(0.602) 1165.914 Polypharmacy+Tar get Medication N=751 KP STATE Model Chi-square*** 0.964(0.063) 0.999(0.932) 199.259 0.973(0.055) 0.995(0.066) 250.669 0.966(0.176) 0.981(0.369) 291.172 Failing Health N=746 KP STATE Model Chi-square*** 0.946(0.103) 1.014(0.586) 262.154 0.960(0.062) 1.005(0.790) 369.653 0.969(0.395) 1.000(0.993) 534.040 High Risk N=3,752 KP STATE Model Chi-square*** 0.970(0.020)* 0.994(0.543) 765.002 0.980(0.018)* 1.002(0.693) 985.386 0.967(0.045)* 0.980(0.134) 1323.016 Low Risk N=l,270 KP STATE Model Chi-square*** 1.156(0.022)* 1.018(0.718) 189.250 1.124(0.028)* 1.009(0.834) 152.696 1.113(0.209) 0.856(0.082) 780.837 Results are all based on full model analysis * P<0.05 ** P<0.01 *** P<0.0001 87 R eproduced with perm ission of the copyright owner. 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Table 12: Results of Time-dependent “As-Treated” Cox model and “Intent to Treat” Cox model (Death Event) Population Estimated Risk Ratio and ( P Value) Regressors Time-dependent Cox Model Intent to Treat Cox Model Total Sample KP 0.921(0.002)** 0.754(0.352) N=5,499 STATE 1.000(0.980) 1.187(0.522) Model Chi-square*** 626.651 463.389 Target Medication KP 0.840(0.004)** 0.509(0.241) N=3,102 STATE 1.017(0.582) 1.089(0.174) Model Chi-square*** 326.888 234.060 Polypharmacy+Tar KP 0.929(0.089) 0.743(0.548) get Medication STATE 0.974(0.442) 0.807(0.621) N=751 Model Chi-square*** 162.905 133.147 Failing Health KP 0.902(0.075) 0.312(0.048)* N=746 STATE 0.938(0.171) 0.488(0.135) Model Chi-square*** 150.363 93.383 High Risk KP 0.922(0.007)" 0.599(0.152) N=3,752 STATE 0.996(0.827) 0.965(0.908) Model Chi-square*" 519.129 390.541 Low Risk KP 1.963(0.008)** 3.388(0.205) N=l,270 STATE 1.314(0.185) 1.352(0.756) Model Chi-square*** 143.361 82.355 * P<0.05 ** P<0.01 *** P<0.0001 8 8 R eproduced with perm ission of the copyright owner. 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Table 13: Results of Time-dependent “As-Treated” Cox model and “Intent to Treat” Cox model (Urgent/Emergency Admission) Population Sample Size Estimated Risk Ratio and ( P Value) Regressors Time-dependent Cox Model Intent to Treat Cox Model Total Sample KP 0.972(0.078) 0.841(0.087) N=5,499 STATE 0.987(0.347) 0.869(0.167) Model Chi-square*** 1964.836 657.149 Target Medication KP 0.945(0.021)* 0.733(0.021)* N=3,102 STATE 0.990(0.602) 0.800(0.100) Model Chi-square*** 1165.914 278.369 Polypharmacy+Tar- KP 0.966(0.176) 0.767(0.197) get Medication STATE 0.981(0.369) 0.921(0.676) N=751 Model Chi-square*** 291.172 158.853 Failing Health KP 0.969(0.395) 0.649(0.086) N=746 STATE 1.000(0.993) 0.534(0.018) Model Chi-square*** 534.040 223.731 High Risk KP 0.967(0.045)* 0.837(0.111) N=3,752 STATE 0.980(0.134) 0.878(0.240) Model Chi-square*** 1323.016 478.937 Low Risk KP 1.113(0.209) 1.384(0.328) N=l,270 STATE 0.856(0.082) 0.876(0.709) Model Chi-square*** 780.837 161.043 * P<0.05 ** P<0.01 *** P<0.0001 89 R eproduced with perm ission of the copyright owner. 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Table 14: Results of Time-dependent Models with Informative Censoring Assumption (Event : Death) Population (% Censoring) Regressors Estimated Risk Ratios and ( P Value) Daily Assumptionl Assumption2 Total Sample KP 0.921(0.002)** 0.975(0.128) 0.920(0.002)** (7.22%) STATE 1.000(0.980) 0.993(0.580) 1.001(0.949) Target Only KP 0.840(0.039)* 0.982(0.480) 0.840(0.004)** (7.22%) STATE 1.017(0.582) 0.986(0.416) 1.017(0.575) Polypharmacy+T arget KP 0.929(0.089) 0.922(0.014)* 0.929(0.087) (4.38%) STATE 0.974(0.442) 0.977(0.369) 0.974(0.436) Failing Health KP 0.902(0.075) 0.884(0.003)** 0.904(0.075) (14.51%) STATE 0.938(0.171) 0.938(0.020)* 0.939(0.176) High Risk KP 0.922(0.007)** 0.976(0.160) 0.922(0.007)** (5.73%) STATE 0.996(0.827) 0.997(0.787) 0.997(0.876) Low Risk KP 1.963(0.008)** 1.187(0.018)* 1.947(0.008)** (9.43%) STATE 1.314(0.185) 1.093(0.153) 1.303(0.193) Assumption 1 ; Censored cases are at the highest level of risk (theoretical assumption, but it is a case in this study, censored cases are known to be still alive in the follow-up period, we only need assumption 2 in this part of analysis) Assumption 2: Censored cases are at the lowest level of risk * P<0.05 ♦ * P<0.01 90 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 15 : Frequency of Urgent/Emergency Admission during 2 Year Demonstration Period N Frequency Percent Cumulative Frequency Cumulative Percent 1 420 70.9 420 70.9 2 86 14.5 506 85.5 3 37 6.3 543 91.7 4 27 4.6 570 96.3 5 1 1 1.9 581 98.1 6 4 0.7 585 98.8 7 4 0.7 589 97.5 9 1 0.2 590 99.7 13 1 0.2 591 99.8 15 1 0.2 592 100.0 91 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 16: Results of Second Hospitalization Impacts of Alternative Pharmacist Models in Subgroup Analysis (Full Model) Population # of Event Regressors Estimated Risk Ratio and ( P Value) Time-dependent Cox Model (Full Model) Total Sample KP 0.866(0.069)* N=592 172 STATE 1.010(0.840) Model Chi-square*** 167.434 Target Medication KP 0.926(0.478) N=335 91 STATE 1.028(0.682) Model Chi-square 69.441 Polypharmacy+Tar- KP 0.792(0.095) get Medication 64 STATE 0.926(0.500) N=168 Model Chi-square*** 101.759 Failing Health KP 0.963(0.783) N=lll 45 STATE 1.037(0.746) Model Chi-square 60.749 High Risk KP 0.869(0.079)* N=492 155 STATE 1.026(0.601) Model Chi-square*** 126.160 Low Risk KP 1.000(0.993) N=65 12 STATE 1.546(0.521) Model Chi-square 23.058 * P<0.05 ** P<0.01 *** P<0.0001 a P<0.05 for comparison of KP and State models 92 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. C D ■D O Q . C g Q . ■ D CD C /) o' 3 CD 8 CD 3. 3 " CD CD ■ D O Q . C a o 3 ■ D O CD Q . ■ D CD C /) C /) Table 17: The Switching Pattern in Kaiser Permanent/USC Pharmacists’ Consultation Intervention Study Original Assignment On- Treatment 200 days 400 days 600 days Last day >50%* >80% 100% >50% >80% 100% >50% >80% 100% >50% >80% 100% KP 5.0% 2.0% 1.9% 2.95 1.0% 0.6% 2.1% 0.5% 0.3% 2.1% 0.5% 0.3% Control Model State 35.8% 23.2% 21.0% 35.8% 19.0% 14.8% 36.0% 18.7% 12.8% 36.4% 18.6% 12.3% Control 45.3% 29.6% 25.5% 44.4% 23.6% 15.9% 42.9% 21.8% 11.9% 41.7% 19.8% 10.1% KP 35.8% 24.2% 21.2% 34.7% 17.5% 11.8% 32.1% 14.9% 7.6% 30.0% 13.0% 6.4% KP Model State 31.6% 20.2% 18.5% 32.0% 16.0% 12.3% 32.85 15.4% 10.7% 34.5% 15.3% 10.2% Control 17.4% 9.6% 8.4% 15.5% 6.0% 3.9% 14.1% 4.5% 2.4% 13.7% 4.0% 1.9% KP 4.9% 2.1% 2.0% 3.7% 1.1% 0.8% 3.2% 0.8% 0.5% 3.2% 1.0% 0.5% State Model State 65.1% 53.0% 49.1% 67.0% 48.8% 38.8% 67.5% 46.2% 34.0% 67.0% 45.9% 31.9% Control 15.6% 8.5% 7.4% 14.2% 5.4% 3.6% 13.6% 4.5% 2.2% 12.8% 4.1% 2.0% * >50% means the percentage of patients who have more than 50% of their new prescriptions filied at a specific pharmacy model during a certain period; >80% means the percentage of patients who have more than 80% of their new prescriptions filied at a specific pharmacy model during a certain period; 100% m eans the percentage of patients who have all of their new prescriptions filled at a specific pharmacy model during a certain period. 93 s 9 m R s6e)uaaj8d aA!$e|nijuno S & R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. C D ■D O Q . C g Q . ■ D CD Chart I I : Survival Impacts of Alternative Pharmacy Intervention M odels by Risk Groups C/) W o' 3 0 3 CD 8 ( O ' 3 " 1 3 CD "n c 3. 3 " CD CD ■ D O Q . C a o 3 ■ D O CD Q . 1 — gggge * * j ■ ■ * Total Sanple Target Medicticn Only Mypharmacy + Target Medication 1%#% Health HghRtekDruge Low R tek ■ D CD C/) C/) - 2 0 . 0 0 % - 1 0 . 0 0 % a c o % 10.00% 20.00% 30.00% Risk Reduction BKPModel ■ Stale Model 40.00% 50.00% 60.00% * PO.06 * * PO.01 Bror bar ; 95% Confidence hterval 95 C D ■D O Q . C g Q . ■ D CD C/) C/) CD 8 CD 3. 3 " CD CD ■ D O Q . C a O 3 " O O CD Q . ■ D CD C/) C/) C hart I I I : Hospitalization Im pacts of Alternative Pharm acist Intervention M odels by Risk Groups (U rgent Admission) -30.00% -25.00% -20.00% -15.00% -10.00% -5.00% Risk Reduction 0.00% Total Sample Target Medctlon Only Polypharmacy + Target Medication Failing Health High Risk Drugs Low Risk EKP Model B State Model 5.00% 10.00% * P<0.05 * * P<0.01 Erro Bar: 95% Confidence interval 96

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Asset Metadata

Creator Yuan, Yong (author)

Core Title Time dependent survival analysis of Kaiser Permanente/USC pharmacists' consultation intervention study

Degree Doctor of Philosophy

Degree Program Pharmaceutical Economics and Policy

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

Tag Health Sciences, Pharmacy,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-625039

Unique identifier UC11340188

Identifier 3110963.pdf (filename),usctheses-c16-625039 (legacy record id)

Legacy Identifier 3110963.pdf

Dmrecord 625039

Document Type Dissertation

Rights Yuan, Yong

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA