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Estimation of heterogeneous average treatment effect-panel data correlated random coefficients model with polychotomous endogenous treatments
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Estimation of heterogeneous average treatment effect-panel data correlated random coefficients model with polychotomous endogenous treatments
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Content
ESTIMATION OF HETEROGENEOUS AVERAGE TREATMENT EFFECT-
PANEL DATA CORRELATED RANDOM COEFFICIENTS MODEL WITH
POLYCHOTOMOUS ENDOGENOUS TREATMENTS
by
Aniket Arun Kawatkar
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
in Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHARMACEUTICAL ECONOMICS AND POLICY)
May 2009
Copyright 2009 Aniket Arun Kawatkar
ii
Dedication
Dedicated to my family for their love, support, and prayers. You have always
been my strength. My mother, Archana A. Kawatkar, and my father Arun B.
Kawatkar, are a source of inspiration, foresight, and guidance. I want to thank them
for everything that they have sacrificed for me and my brother. I am blessed to have
them as my parents. I also want to thank my brother, Sachin A. Kawatkar, for his
unwavering support and help.
Special thanks go to my wife, Ami A. Kawatkar, who has helped me navigate
through many difficult times by providing the strength and determination to
persevere in my goals. She is my true friend, and a magnificent companion. Last but
certainly not the least; I want to thank my daughter and bundle of joy, Aariya A.
Kawatkar. Her beautiful smile brings sunshine to my life.
iii
Acknowledgements
I am immensely grateful to my advisor and dissertation chair Dr. Michael B.
Nichol. I am especially appreciative for his guidance and enthusiastic support not
only in writing this dissertation but during my entire academic tenure at USC. I have
learnt a lot under his proficient mentoring and unwavering support towards my
academic goals. I am thankful to him for providing many diverse research projects
through which I have gained invaluable didactic and multi-tasking skills.
I have greatly benefited from Dr. Joel Hay’s and Dr. Jeonghoon Ahn’s
constructive suggestions and scholarly comprehension of econometrics. Dr. William
Stohl refined my clinical understanding and provided erudite suggestions about real
life treatment decisions in rheumatoid arthritis. Dr. Jason Doctor provided helpful
suggestions to elucidate my proposal. I am highly obliged to all of you. I sincerely
appreciate your critical insights which have made this dissertation more elegant and
scientifically rigorous.
I am thankful to Dr. Jeffrey McCombs for his support and guidance during
my entire tenure at USC. I am deeply thankful to Joanne Wu for her tremendous help
in creating the Medi-Cal data analytical file. I would also like to thank my colleagues
who have shared this ardent journey to the dissertation.
iv
Table of Contents
Dedication. . . . . . . . . ii
Acknowledgements. . . . . . . . iii
List of Tables. . . . . . . . . vi
List of Figures. . . . . . . . vii
Abstract. . . . . . . . . viii
Chapter 1 Introduction. . . . . . . 1
Chapter 2 Background, Literature Review and Conceptual Model. . 5
2.1 Background / Significance. . . . . . 5
2.1.1 Epidemiology and Etiology. . . . . 5
2.1.2 Burden of Disease. . . . . . . 7
2.1.3 Quality of Life of Rheumatoid Arthritis Patients. . . 8
2.1.4 Productivity Loss in Rheumatoid Arthritis. . . . 10
2.1.5 Pharmacologic Treatment for Rheumatoid Arthritis. . 10
2.1.6 Treatment Costs for Rheumatoid Arthritis. . . . 17
2.1.7 Endogeneity in Estimating Treatment Effect of
Biologic DMARDs. . . . . 20
2.2 Econometrics Literature on Selection Bias. . . . 23
2.2.1 Methods for Correcting Selection Bias. . . . 23
2.2.2 Applications of Sequential Decision,
Polychotomous Choice and IIA. . . . . 25
2.2.3 Note on Potential Outcomes Framework,
Instrumental Variables, Propensity Scores
and Regression Discontinuity Designs. . . . 30
2.2.4 Characteristics of Cost/Expenditure Data. . . . 34
2.3 A Conceptual Model for Evaluation of Treatment Effect. . 39
Chapter 3 Study Design and Methods. . . . . 58
3.1 Data. . . . . . . . . 58
3.2 Patient Sample. . . . . . . . 59
3.3 Expenditure and Covariates. . . . . . 65
3.3.1. Quarterly expenditure. . . . . . 65
3.3.2. Covariates. . . . . . . . 66
3.3.3. Treatment Indicators. . . . . . 69
3.4 Methodology . . . . . . . 70
v
Chapter 4 Results. . . . . . . . 73
4.1 Descriptive Statistics. . . . . . . 74
4.1.1 Distribution of Demographic Variables. . . . 74
4.1.2 Distribution of Comorbidities and Exclusion Restrictions. . 75
4.1.3 Distribution of Episode Expenditures. . . . 75
4.2 Likelihood Ratio Test for Selection Model. . . . 76
4.3 Multicollinearity Due to the Generalized Residual. . . 77
4.4 Presence of Time Varying Endogeneity. . . . 78
4.5 Estimation of ATE1 or Homogeneous ATE. . . . 79
4.6 Estimation of Heterogeneous ATE. . . . . 83
Chapter 5 Discussion. . . . . . . . 87
References. . . . . . . . . 101
Appendix A. . . . . . . . . 117
Appendix B. . . . . . . . . 118
Appendix C. . . . . . . . . 119
Appendix D. . . . . . . . . 120
Appendix E. . . . . . . . . 121
vi
List of Tables
Table 2.1: Pharmacy Cost/Charges for DMARDs. . . . 19
Table 2.2: Types of Discrete Choice Models and
their Error Distributions. . . . . . 48
Table 4.1: Distribution of Demographic Covariates. . . . 74
Table 4.2: Distribution of Comorbidities and Exclusion Restrictions. 75
Table 4.3: Distribution of Quarterly/Episode Total Expenditures. . 76
Table 4.4: Treatment Selection Choice Model. . . . 77
Table 4.5: Correlation between Generalized Residual
and Exogenous Variables. . . . . . 78
Table 4.6: Estimate and Significance of Generalized Residual. . 79
Table 4.7: Estimates of ATE1 Standard DMARD vs. Adalimumab. . 80
Table 4.8: Estimates of ATE1 Standard DMARD vs. Etanercept. . 81
Table 4.9: Estimates of ATE Standard DMARD vs. Adalimumab. . 83
Table 4.10: Estimates of ATE Standard DMARD vs. Etanercept. 84
vii
List of Figures
Figure 3.1: Illustration of Study Design and Definitions. . . 61
Figure 3.2: Cohort Diagram of Inclusion/Exclusion Criteria. . 63
Figure 4.1: Graph Homogeneous Average Treatment Effect. . 82
Figure 4.2: Graph Heterogeneous Average Treatment Effect . 82
Figure 4.3: Graph Comparing ATE to ATE1 in Adalimumab. . 86
Figure 4.4: Graph Comparing ATE to ATE1 in Etanercept. . . 86
viii
Abstract
We estimated the treatment effects of biologic disease modifying anti-
rheumatoid drugs (DMARDs) on the quarterly total health-care expenditure, while
controlling non-random assignment to treatment (endogeneity) and allowing
heterogeneity in treatment effects. The structural parameters, heterogeneous (ATE),
and homogeneous (ATE1) average treatment effects were defined as the impact of
treatment on quarterly total health-care expenditure, if patients are randomly
assigned to biologic DMARDs.
A retrospective cohort was selected from California Medicaid paid claims
between 01/01/1999 and 12/31/2005. Non-overlapping quarters were created from
pharmacy claims for biologic (adalimumab and etanercept) and standard
(leflunomide, hydroxychloroquine and sulfasalazine) DMARDs. Final sample
included 23,297 observations on 5,239 individual patients.
A fixed-effects panel data correlated random coefficients (CRC) model
allowed for heterogeneity in treatment effects. Endogeneity was controlled by adding
a generalized residual function constructed based on Lee’s (1983) approach.
Selection choice model was varied from the multinomial, nested, and mixed logit.
Controlling endogeneity significantly increased ATE1 for both biologic
DMARDs, as compared to naïve fixed-effects (baseline standard DMARD). Nested-
logit based ATE1 was higher as compared to the multinomial-logit ATE1. Allowing
for unobserved heterogeneity resulted in the ATE of adalimumab to decrease under
the multinomial-logit corrected model, while an increase was observed in the
ix
nested-logit corrected model. In case of ATE for etanercept, an increase was
observed under both the above mentioned models as compared to ATE1.
The results point out the need to control for time-varying endogeneity in
panel data models. When treatment effects are heterogeneous and especially when
treatment selection is a discrete choice set, the specification of latent index model
matters. Sorting on gains is an important source of bias in medical outcomes and in
this study, it manifested in terms of large differences in the magnitude of ATE1 and
ATE parameters, which questions homogeneity assumption.
The methodological issues addressed in this study impact our understanding
of the cost effects of drug treatment. Models need to be realistic to mimic real life
clinical decisions to inform important drug coverage decisions. Panel data CRC
model with endogeneity correction is one such tool to assess comparative
effectiveness using an observational study design for expenditure outcomes.
1
Chapter 1
Introduction
Rheumatoid arthritis (RA) is an auto immune syndrome in which the
synovium or lining of the joints is inflamed. It is a painful chronic disease with high
burden of illness and no cure, often leading to disability and early mortality. Even
the state-of-the-art treatments can only reduce or prevent future damage to the bones
and joints. Currently, there is no single or combination therapy which can reverse the
existing bone/cartilage damage. Moreover, even the preventive effect of the new
disease modifying anti-rheumatoid drugs is transient.
Many drugs have been approved for “controlling” this disease or for
palliative purposes. However, a single therapeutic agent generally never succeeds in
controlling disease progression and with the failure of first line agents; second line
treatment is initiated to control the disease. Second line agents used in RA, in
particular, the biologic response modifying agents are invariably expensive and
hence, an assessment of economic validation is crucial for rational allocation of
scarce healthcare resources. The research question for this study was to estimate the
treatment effects (TE) of using biologic response modifying agents on the economic
outcome of quarterly aggregate expenditure of RA patients.
Comparison between the second line agents is intricate since, most of them
are indicated to be used, based on presence or absence of certain prognostic factors.
In addition, physician’s choice of treatment is generally based on patient’s
2
preferences regarding the treatment options, route and frequency of drug
administration, and the recommended treatment guidelines in existence
(Cush 2005; Wolfe and Michaud 2007). Financial considerations are also found to
influence physicians’ prescription decisions and consequently health care costs
(DeWitt et al. 2006). Most of these treatment choice variables are not available in
majority of the state/nationally representative datasets and hence, significant
selection/endogeneity bias complications have to be accounted before assessing the
economic impact to the payer. A majority of current economic analyses make use of
traditional endogeneity correction techniques to adjust for the non-random
assignment to treatment prevalent in retrospective studies. Secondly, in an
observational analysis using secondary data on insurance claims, there is a potential
for another source of bias in the parameter estimates. This second bias is due to the
correlation of the endogenous treatment variable(s) with the estimated treatment
parameters, a phenomenon described as heterogeneity in treatment effects. When
adoption/rejection of treatment decisions are based on these individual
idiosyncrasies, heterogeneity in treatment effects needs to be controlled in order to
obtain an unbiased estimate of the treatment effect. In existing literature, even if
correction for endogeneity in treatment assignment is employed, most studies fail to
account for the heterogeneity in treatment effects. Accounting for this heterogeneity
is important in any medical outcomes analysis as it impacts estimated parameters.
Specifically for this study, heterogeneity in the treatment effect is defined as the
partially unobserved idiosyncratic differences at the patient level which determine
3
participation in the treatment. Failure to control for the endogeneity in treatment
assignment and heterogeneity in the treatment effects will result in the estimated
treatment effects being biased even asymptotically (Heckman et al. 2006).
Lastly, current literature on methods to correct for endogeneity caused due to
non-random treatment assignment have ignored the importance of the discrete nature
of the treatment variable when comparative effectiveness involves retrospective
head-to-head comparison of multiple treatments. Implementation of instrument
variables and control function based approaches exploiting the discrete choice of
treatment needs sophisticated appreciation of assumption under which estimators
produce consistent estimates. Panel data approaches to these nonlinear discrete
choice-linear outcome structural models are even more complicated than their cross-
sectional versions. However, panel data techniques also offer enhanced methods to
model estimation challenges which are not possible to be addressed in cross-
sectional analysis.
This study will apply advanced panel data econometric methodology to
overcome time varying endogeneity in treatment assignment as well as heterogeneity
in treatment effects which are two important sources of bias affecting parameters of
comparative effectiveness using secondary data on expenditure outcomes. We also
study the impact of varying the assumptions of the choice generation model or the
index function as described in econometrics literature. The methodology presented in
this dissertation will offer enhanced control for endogeneity in choice of multiple
treatments in a panel data setting.
4
The methodology presented has broad applicability to any disease treatment
comparative effectiveness study, involving non-experimental retrospective study
design comparing multiple classifications of treatments.
5
Chapter 2
Background, Literature Review and Conceptual Model
This chapter will describe the background/significance starting with
epidemiology and etiology of rheumatoid arthritis. The next sections describe the
literature on societal impact of rheumatoid arthritis namely, burden of disease,
quality of life of patients, and productivity loss. Following literature summarizes the
pharmacologic treatments available for rheumatoid arthritis and the related treatment
costs.
The econometrics literature review summarizes the existing methods for
correcting selection bias and then describes relevant applications of sequential
decision, polychotomous choice, and the problem of independence of irrelevant
alternatives in choice models. For the present study, we then describe the feasibility
of competing methods such as instrument variables, propensity scores, and
regression discontinuity designs to solve the endogeneity bias. We then describe the
characteristics of cost/expenditure data. Based on the literature, we develop a
conceptual model, in a potential outcomes treatment effects framework, for this non-
experimental comparative effectiveness study of treatment choices for RA.
2.1 BACKGROUND / SIGNIFICANCE
2.1.1 Epidemiology and Etiology
The prevalence of rheumatoid arthritis in United States is estimated to be
around 0.5 to 1% or around 2.1 million (NIH 2004). Women comprise a majority of
these patients with two to three times as many females as males have rheumatoid
6
arthritis (NIH 2004). The disease peaks in the age group of 40 to 70 years but can
occur in children or older adults and it’s been observed that prevalence increases
with age (Lee & Weinblatt 2001; NIH 2004). Incidence rates in United States have
varied from 0.024–0.075% in Caucasians and in recent decades this rate is on the
decline (Kvien 2004).
Arthritis literary means inflammation of joints. Rheumatoid arthritis is an
autoimmune persistent inflammatory disease that causes pain, stiffness, and swelling
around the joints. The immune system attacks cells of the synovium layer which
covers the joints, causing the pain and swelling (NIH 2004). The synovium layer
produces a clear synovial fluid that nourishes the cartilage and the bone. In RA, the
white blood cells attack this synovium layer. As white blood cells react with the
synovial layer they produce cytokines, which are responsible for inflammation (Lee
& Weinblatt 2001; NIH 2004). Prominent cytokines present in large quantities, in
affected synovial fluid and synovial tissue include tumor necrosis factor α (TNF- α)
and interleukin-1 (Lee & Weinblatt 2001). The inflammation causes destruction of
the cartilage and the bone. Mediators to this destruction process are numerous
extracellular factors, including matrix degrading enzymes such as lysosomal
cathepsins, matrix metalloproteinases (MMPs), and membrane type matrix
metalloproteinases (Okada 2001). The failure of developing treatment that
specifically inhibits inflammatory triggers jointly has been attributed to the
uncertainty about which of these triggers contributes most significantly to joint
7
inflammation and destruction, and combined with the fact that several have other
important physiological functions (Breedveld 2004).
The symptoms of RA which include pain, swelling and stiffness of affected
joints are often worse in the mornings and after prolonged periods of inactivity.
Additionally, other vital organ systems may also be affected, occasionally with
potentially life-threatening complications. Chen et al. had reported that patients
frequently experience symptoms of fatigue and hematic abnormalities such as
anemia and increased platelet count. Other reported symptoms in RA patients
included weight loss, lymph node enlargement, pleurisy, pleural effusion, alveolitis,
pericarditis, vascular inflammation (vasculitis), skin nodules, and eye diseases (Chen
et al. 2006).
As the disease advances, patients with rheumatoid arthritis often find their
joints to be rigid and moving inappropriately. As compared to osteoarthritis, the
peculiarity of rheumatoid arthritis is that it causes symmetrical pain in the joints (e.g.
in both knees, both wrists etc) and this is one of its distinguishing features (NIH
2004). Given the prevalence and debilitating symptoms, it is not hard to imagine the
significant societal burden of this disease.
2.1.2 Burden of Disease
Rheumatoid arthritis presents an enormous economic and humanistic burden
on society in terms of the direct medical costs, the indirect costs including lost
wages, and the intangible costs of pain, fatigue, lowered self esteem or other
psychological problems (Kvien 2004). In the year 2003, arthritis and other rheumatic
8
conditions collectively cost the U.S. economy nearly $128 billion ($80.8 billion in
direct and $47.0 billion in indirect costs excluding pain and suffering), equivalent to
1.2% of the 2003 U.S. gross domestic product (CDC MMR 2007). These figures are
an underestimate as this analysis did not account for losses from indirect and
intangible costs since, they were not measured.
Direct costs have been reported to increase exponentially as the disease
progresses (Pugner et al. 2000). In the analysis of one year cost of RA treatment,
ambulatory care ($914/person) was the highest direct medical cost involved in the
treatment of the disease followed by cost of emergency department and
hospitalization ($352/person) (CDC MMR 2007). In contrast, medicines used to treat
RA represented a reasonable proportion (19%) of direct costs (CDC MMR 2007)
with a range between (8-25%) (Yelin & Wanke 1999; Cooper 2000). However,
since, current prescription drugs are not curative, around one-third of RA patients
will require surgery (most often total joint replacement) within 10 years of disease
onset (Kvien 2004). This is also the primary reason for arthritis being the number
one cause of disability in US today with an estimated 50% of the patients unable to
work after 10 years from diagnosis. The indirect societal burden is significant from
the impact on patient’s quality of life, and productivity loss.
2.1.3 Quality of Life of Rheumatoid Arthritis Patients
Nichol & Harada have stressed the importance of measuring health related
quality of life in RA patients due to the lack of reliability of clinical measures in
estimating patient’s condition and also due to the toxicity of the potent drugs used in
9
the treatment of RA (Nichol et al. 1999). Clarke et al. had shown that a clinically
meaningful association exists between radiographic damage and self reported
functional disability (Clarke et al. 2001).
A European study conducted by Smedstad et al. found that functional
disability in RA patients was significantly correlated to gender, age, disease duration,
and disease activity measures such as the erythrocyte sedimentation rate, which
according to them, was an indicator of a deteriorating functional status (Smedstad et
al. 1996). In another study by the same authors evaluating impact of early RA on
mental distress, high levels of disability was associated with a negative impact on the
psychological and social function of the patient, consequently leading to mental
distress, depression and fatigue (Smedstad et al. 1996). The association between high
level of disability and decreased coping ability on mental health was reinforced in
three more studies and warrants incorporating depression treatment in RA patient’s
disease management to reduce future healthcare burden due to psychological issues
(Wright et al. 1996; Smedstad et al. 1997; and Sharp et al. 2001). Other RA
symptoms contributing to mental distress are the combination of pain and disability
(Smedstad et al. 1997). Fatigue also impacts quality of life in RA since, it is a
significant symptom associated with debilitating RA patients (Kvien 2004). Fatigue
has been found to be a contributing factor to work difficulties, personal injury,
reduced ability to participate in rehabilitation programs, and strained relationships
(Belza et al. 1993; Wolfe et al. 1996; Riemsma et al. 1998; Fifield et al. 2001).
10
2.1.4 Productivity Loss in Rheumatoid Arthritis
From the employer’s perspective, Birnbaum et al. estimated the annual per
capita employer expenditures for RA employees with disability to be $17,822 and
that for every $1 spent on direct medical costs by RA employees, the employer spent
$19 on additional direct and indirect costs (Birnbaum et al. 2004). Average
incremental cost for RA-workers irrespective of disability status was $4244 (in 2003
dollars) greater than that of non-RA workers to the employer. In the ranking of most
costly chronic condition per employee, RA was fourth in the list (Ozminkowski et al.
2006).
From the patients’ perspective, as measured by annual household income
loss, the overall decrement in earnings caused by RA was $6,287 (11.8%) according
to Wolfe et al., who further found that earnings and household income were
dependent on functional status, education, age, ethnicity, and marital status. They
also found that income loss was predicted by the Health Assessment Questionnaire
(HAQ), HAQ-II, Modified HAQ, and SF-36 (Wolfe et al. 2005). In a study by
Backman et al., work limitations, was associated with lower functional status, more
pain, and less psychologically demanding work (Backman et al. 2004).
2.1.5 Pharmacologic Treatment for Rheumatoid Arthritis
Non-steroidal anti-inflammatory drugs-
Treatment for RA has improved over the years. Treatment typically used to
start with painkillers to stop the pain caused by inflammation. Non-steroidal anti-
inflammatory drugs (NSAIDs) such as ibuprofen have the advantage of controlling
11
the inflammation associated with RA. However, NSAIDs are associated with
stomach ulcers caused due to adverse effects of these drugs. NSAIDs block the
action of cyclooxygenase (COX-1 and COX-2) enzymes. COX-1 is associated with
the production of stomach mucus lining. As COX-1 production is inhibited by these
drugs, the mucus lining is ruptured causing ulcers. An estimated 13 million people in
US population are using NSAIDs on a habitual basis, which results in annual costs of
hospitalization due to serious GI complications exceeding $1 billion. COX-2 specific
inhibitors such as celecoxib, and valdecoxib reduce the damage to the stomach
lining. The COX-2 specific inhibitors and NSAIDs have shown comparable clinical
efficacy at equipotent doses for the management of acute pain and other conditions
associated with pain. Recently, however, COX-2 selective NSAIDs have been shown
to increase risk of thrombotic cardiovascular events including non-fatal myocardial
infarction and non-fatal strokes, particularly when used at higher doses (ACR 2002).
In view of the same, rofecoxib was voluntarily pulled out of the market by its
manufacturer. The treatments using painkillers, NSAIDs including COX-2 specific
inhibitors however, are not curative and over a period of time as the disease
progresses the bone destruction cannot be controlled.
Standard Disease Modifying Anti-rheumatic Drugs-
The pyramid approach of starting with least expensive medication and
stepping up to the more expensive disease modifying anti-rheumatic drugs has
changed in the past few years. This change had been a result of studies which have
12
reported factors enabling the change in course of RA to be the early referral to
rheumatologist and early aggressive DMARD treatment (Breedveld 2004).
Experience has taught that as time progresses and when the disease gets aggressive,
prognosis gets difficult (Breedveld 2004). Hence, disease-modifying anti-rheumatic
drugs such as methotrexate are used as first choice of treatment either alone or in
combination with other DMARDS such as hydroxychloroquine, sulfasalazine,
cyclosporine, and azathioprine. The positive impact of DMARDs is in their ability to
reduce inflammation, improve functional/disability status in comparison with
NSAIDs in early RA, decrease radiographic progression, provide dosing flexibility,
and availability of excellent data on toxicity and drug interaction profiles (Breedveld
2004). A first line treatment approach may involve DMARDs used in combination or
as monotherapy. Rheumatologist may initiate monotherapy as first line treatment
approach and treatment choice usually involves sequential monotherapy (Breedveld
2004). Combination therapy is generally prescribed in either of the following three
methods: (a) a continuous approach, two or more DMARDs are used simultaneously;
(b) a step-up approach, monotherapy is followed by addition of subsequent
DMARDs if adequate efficacy is not achieved; and (c) a step-down approach, in
which several DMARDs are started at the onset, with the intention of discontinuing
the most toxic or the most expensive, once goals are achieved (Breedveld 2004).
However, these disease modifying drugs also have certain limitations.
Methotrexate can cause serious liver and lung toxicity above a certain dosage.
Patients cannot continue even the social use of alcohol (Kremer 2001). Cure of the
13
disease in patients using these drugs is uncommon. Methotrexate cannot be used in
patients with certain preexisting liver, kidney, or lung disease (Kremer 2001). Many
patients are unable to endure elevated doses of methotrexate to achieve an optimal
therapeutic benefit (Kremer 2001). In general, the DMARDs have a delayed onset of
action (1–6 months in most cases) and some of them have less proven effectiveness
on radiographic disease progression and health related quality of life. DMARDs also
require close monitoring because of the possibility of multiple toxicities. The dosing
regimen of DMARDs is difficult and complex without long term sustainability and
rarely yields treatment free remissions (Breedveld 2004).
Biologic Response Modifying Agents -
The new biologic agents including the tumor necrosis factor (TNF) inhibitors
are showing good results in controlling RA. These biologic agents however, are
extremely expensive and hence, demand optimal utilization for maximum benefits.
Presently, all these so called biologic response modifiers are extremely expensive as
compared to standard DMARD therapy. Hence, it is very important to study their
cost effectiveness and to ascertain optimal utilization for maximum social welfare.
At present, there are 3 approved TNF inhibitors namely, etanercept, infliximab and
adalimumab. The biologic agents list also includes monoclonal antibodies directed
against interleukin-1 receptor (anakinra), CTLA-4 (abatacept) and CD20 on B-cells
(rituximab). However, as abatacept and rituximab came later in the market, the data
available for this study might not contain enough observations on their utilization to
realistically estimate the treatment effect of these drugs on the cost of healthcare. For
14
the purposes of this study, the estimation of treatment effect on cost of health care
will be limited to the three TNF inhibitors and the interleukin-1 receptor inhibitor
anakinra.
All the three TNF inhibitors have different mechanisms of action but do the
same work, which is to block the tumor necrosis factor and consequently reduce
inflammation. Infliximab is a partially humanized mouse monoclonal antibody
inhibiting the action of TNF- α but not TNF- β (Lee & Weinblatt 2001). Etanercept is
an artificial bioengineered molecule, whereas adalimumab is fully human anti-TNF –
α monoclonal antibody. All three TNF inhibitors are administered as injections.
Anakinra is a recombinant human IL-1 receptor antagonist, which works by binding
to the type I IL-1 receptors. Specifically it blocks IL-1, a proinflammatory cytokine,
from activating effector cells, such as monocytes and macrophages, fibroblasts,
chondrocytes, and osteoclasts (Gabay & Arend 1998).
Abatacept on the other hand is a recombinant fusion protein, consisting of the
extracellular sequence of human CTLA-4 and the Fc domain of human
immunoglobulin G1 (IgG1), modified to prevent complement fixation (Pucino et al.
2006). Lastly, rituximab is a chimeric monoclonal antibody that depletes immature
and mature B cells excluding plasma cells that have CD20 on their surfaces (Pucino
et al. 2006).
Infliximab was one of the first biologic DMARDs to get FDA approval based
on randomized trials which showed that more than half of patients on infliximab had
a 20% improvement in ACR score and around 30% of these patients had a 50%
15
improvement over a period of 30 weeks, which was significantly higher than patients
on placebo (Maini et al. 1998; Maini et al. 1999; Kavanaugh 2000; and Lipsky et al.
2001). This response to infliximab was maintained for 54 weeks and the proportion
of patients with a 20% improvement in ACR was in the range of 42–59% in all
infliximab treatment groups (Maini et al. 1998).
In safety and efficacy trials, treatment with etanercept resulted in significant
dose-related reductions in disease activity. After 3 months and 6 months changes
were significant in ACR 20, ACR 50 and ACR70 scores as compared to controls at
different doses (Moreland et al. 1997; Moreland et al. 1999). The long-term efficacy
and safety of etanercept monotherapy in patients with DMARD-refractory RA was
demonstrated in open-label extension studies lasting up to 5 years (Moreland et al.
2001; Moreland et al. 2002). Etanercept in combination with methotrexate showed
significant differences in ACR 20 and ACR 50 scores between the treatment and
control groups (Weinblatt et al. 1999). In treating early RA, etanercept was
compared to methotrexate. Results indicated significant differences within first 6
months but were approximately similar after 6 months (Bathon et al. 2000).
Treatment with adalimumab produced dose-related disease improvements
measured by ACR20, ACR50, and ACR70 response criteria, with the monoclonal
antibody demonstrating superiority to placebo at all dosages (de Putte 2003).
Adalimumab was safe and well tolerated in the randomized clinical trials as well as
in the open label studies that followed (Kavanaugh 2002; de Putte 2003). Common
adverse events observed included injection-site reactions, rash and
16
headache (de Putte 2003). In a study evaluating the combined effect of adalimumab
and methotrexate, ACR20 and ACR 50 responses at 24 weeks were attained by a
significantly greater percentage of patients in the adalimumab plus methotrexate
groups as compared to the placebo groups. These effects were sustained for 12
months in patients receiving adalimumab 40 mg s.c. every other week in
combination with methotrexate (Keystone et al. 2001). Other studies have shown
significant differences in radiographic end points between the adalimumab-treated
and placebo groups after 1 year (Keystone et al. 2002).
Randomized trials involving anakinra have shown it to be significantly more
effective than placebo in producing ACR-20, ACR-50, and ACR-70 responses in
patients who had failed methotrexate. Anakinra was also effective when given in
combination with methotrexate to patients who have had an inadequate response to
methotrexate alone (Cohen et al. 2004). Bresnihan et al. found that anakinra
monotherapy was significantly more effective than placebo in slowing radiographic
joint damage at 24 weeks, as signified by meaningful reductions in the total modified
Sharp score (Bresnihan et al. 2004). They further reported that this treatment effect
was even more pronounced in patients who continued anakinra for an additional 24
weeks.
Combination DMARD Therapy-
Studies which combined methotrexate with cyclosporine (Tugwell et al.
1995); infliximab (Maini et al. 1998; Maini et al. 1999; and Lipsky et al. 2001);
etanercept (Weinblatt et al. 1999); leflunomide (Weinblatt et al. 1999); sulfasalazine
17
and hydroxychloroquine (O’Dell et al. 1996); sulfasalazine and prednisolone
(Boers
et al. 1997); and sulfasalazine, hydroxychloroquine, and prednisolone (Mottonen et
al. 1999), have reported that combination therapy has higher benefits and much more
tolerable toxic effects as compared to monotherapy. Combination therapy benefited
patients with new onset of symptoms and even those with several years of disease
duration and who had failed previous DMARD therapy. These results support
aggressive therapy approach in patients in any of the stages of disease progression.
Recent trials also support slowing of joint erosions with combination therapy; (Boers
et al. 1997; Lipsky 1999; Mottonen et al. 1999; and Lipsky et al. 2001) suggesting
that concurrent use of several DMARD agents is a valid form of disease management
(Lee & Weinblatt 2001). The combination therapies that were intended to be focused
in this study included: methotrexate + infliximab, methotrexate + etanercept,
methotrexate + adalimumab, methotrexate + hydroxychloroquine; and anakinra or
methotrexate + anakinra (Grijalva et al. 2007).
2.1.6 Treatment Costs for Rheumatoid Arthritis
Gabriel et al. found a significant difference in rheumatologist care as
compared to generalist care in the number of radiographs for primary care of RA
patients; however, there was no difference in terms of treatment costs of RA (Gabriel
et al. 2001). Medications constitute the second largest component of RA-related
costs accounting for around 8-24% of total medical cost (Cooper 2000).
Amongst the medications, DMARDs are responsible for about two-thirds of
the total drug cost and NSAIDs for most of the remainder (Yelin & Wanke 1999).
18
However, the expenditure pattern in managed care was reported to be very different
with 62% spent on prescription medications, 21% to ambulatory care, and 16% to
hospital and emergency room care (Lanes et al. 1997). The Lanes et al. study is an
aberration as most US and European studies have shown median prescription
medicine use to be around 16% (Range 7% -20% excluding Lanes et al.) of direct
medical cost (Pugner et al. 2000; CDC MMR 2007).
The introduction of the expensive biologic DMARDs in RA has been
associated with the greatest increase (50%) in pharmacy spending from 2003 to 2004
(Pucino et al. 2006). This escalation in expenditure has increased the interest in
comparative analysis of biologic DMARDs with standard DMARDs and also within
each class of drugs. Griffith et al. compared the average monthly cost of RA care for
the standard DMARDs and found the mean overall cost to be $853, of which $294
(34%) was for RA-related medical services. Comparing the monthly RA- related
costs between the standard DMARDs, Griffith et al. reported the lowest cost for
hydroxychloroquine ($227; n = 252), sulfasalazine ($233; n = 49), methotrexate
($340; n = 185); and highest for other mono/combination therapy ($425; n = 85)
(Griffith et al. 2000).
Comparing standard and biologic DMARDs, Yazdani et al. have reported
that RA patients treated with etanercept $7722 (SD=$5285) had statistically higher
mean 6-month post diagnosis charges than leflunomide $3301 (SD=$4054)
recipients and this difference was attributed to statistically higher RA-related
pharmacy charges for etanercept $5877 (SD=$2237) as compared to leflunomide
19
$1877 (SD=$1258) (Yazdani et al. 2001). The weakness of their analysis was the use
of “charges” as opposed to “cost” of treatment since, charges do not account for
discounts and rebates offered for the branded medications.
Table 2.1 Pharmacy Cost/Charges for DMARDs
Drug Name Cost/Charge (±SD) Reference
Hydroxychloroquine $227 (±268) - Average monthly cost
Sulfasalazine $233 (±278) - Average monthly cost
Methotrexate $340 (±575) - Average monthly cost
Griffith et al.
2000
Etanercept* $5877 (±2237) - 6-month costs
Leflunomide* $1877 (±1258) - 6-month costs
Yazdani et al.
2001*
Infliximab $13,470 – Annual cost Gilbert et al.
2004
* Although the results are reported as “cost”, this study has used “charges” and “cost” interchangeably
Due to the lower cost of medications in the managed care setting, costs of
RA-related care were 42% lower among leflunomide ($9618) patients as compared
to etanercept ($16,534) and 53% lower as compared to infliximab ($20,263)
(Ollendorf et al. 2002). The analysis further stratified total costs according to
whether patients received pretreatment methotrexate, to examine the possible impact
of prior drug failure restrictions on treatment effect. The stratified analysis reported
higher costs among patients who had failed prior methotrexate treatment as
compared to methotrexate naïve group. However, even in the subgroup analysis,
mean total costs remained lower among leflunomide patients ($12,506 versus
$18,330 and $23,237 for etanercept and infliximab, respectively), and in the group of
patients who did not receive pretreatment methotrexate ($7023 versus $14,870 and
$17,250, respectively) (Ollendorf et al. 2002).
A significant issue with estimation of treatment effects in RA is that of
confounding due to dose escalation which is common in RA. Gilbert et al. have
20
reported that nearly 60% of infliximab patients increased dosage at the end of one
year, compared to only 18% dose escalation observed in etanercept. Furthermore,
infliximab patients who escalated dose incurred a 25% increase in mean one-year
costs ($20,915 vs. $16,713 for no increase; p < 0.0001). However, costs among
etanercept patients did not substantially differ based on dose escalation ($14,482 vs.
$13,866 respectively) (Gilbert et al. 2004).
Comparing between the biologic DMARDs, Gilbert et al. further reported
that the overall costs for patients initiating infliximab therapy were higher than for
patients in the etanercept group ($19,144 vs. $13,977) and much of the difference
was due to the difference in drug costs (infliximab ($13,470) vs. etanercept
($10,159) respectively). Furthermore, infliximab patients had higher costs for
physician management visits ($691 vs. $381), ancillary services ($1,511 vs. $866),
and hospitalizations ($2,277 vs. $1,322) (Gilbert et al. 2004).
These results were reiterated in patients aged 65 and above; Weycker et al.
have reported mean total cost of RA-related care was lower for etanercept patients in
two databases they analyzed; $12,159 (95% CI =$10,795-$13,380) for etanercept vs.
$22,347 (95% CI = $20,808-$23,912) for infliximab in one, and $14,297 (95% CI =
$12,238-$16,326) for etanercept vs. $22,154 (95% CI = $19,688-$24,703) for
infliximab in the other dataset (Weycker et al. 2005).
2.1.7 Endogeneity in Estimating Treatment Effect of Biologic DMARDs
Due to the non-random assignment to treatment in the current observational
study, the process of selecting between the biologic agents gives rise to endogeneity.
21
Treatment selection amongst the biologic DMARDs should be based on logistics,
patient willingness or aversion to various medication delivery systems,
contraindications, co-morbidities, concomitant medications, susceptibility to
infection, and other factors which are unique for each patient (ACR Position
Statement 2006). Most of these treatment selection variables are not observable in
insurance claims data and these variables are correlated to the models treatment
effect indicator. This correlation between the explanatory variables and the error
term makes the parameter estimates biased since, the regression coefficients
incorrectly explain the variance associated with these correlated omitted variables.
Econometric methods to correct for this endogeneity caused due to the so called
“selection on unobservables” problem have relied on instrument variables and
control function approaches. Both these techniques rely on the existence of
instrument variable(s) which are uncorrelated to the error, correlated (strongly) to the
endogenous variable and have no direct effect on the outcome of interest.
Technically though, the control function method can identify the parameters of
interest even in the absence of identifying exclusions (also called rank condition), if
the selection equation describing the treatment choice is nonlinear. Leading case of
this selection equation in literature is the probit model for the binary endogenous
case and multinomial logit for the polychotomous endogenous regressor. This brings
us to the second weakness in the existing methods prevalent in literature.
A point that distinctly stands out in treatment selection is that some of the 2
nd
line drugs are viewed as closer substitutes for one another than other drugs e.g.
22
substitution amongst biologic DMARDs as compared to substitution between
standard DMARDs and biologic DMARDs. Indeed it is reasonable to assume that
when selecting a drug, physicians view drugs within a class to be closer substitutes
for each other as compared to drugs from another classification category. Failure to
account for this correlation amongst the alternatives gives rise to the independence of
irrelevant alternatives (IIA) problem (McFadden 1981).
The traditional endogeneity correction models however, fail to account for
this correlation amongst the treatment choices and thus ignore the independence of
irrelevant alternatives (IIA) problem in the selection equation (also called the
indicator/index function which describes the latent choice model). Hence, a discrete
choice modeling procedure that relaxes the IIA assumption of multinomial logit and
also accounts for correlation amongst the treatment choice of biologic DMARDs is
more appropriate in the current study. To evaluate the economic impact of the 2
nd
line agents that have similar cross-elasticities of substitution, modeling 2
nd
line
treatment choice needs to be carried out using a flexible approach relaxing the IIA
assumption. Advances in discrete choice modeling such as the nested logit, the
mixed logit, the multinomial probit, and the heteroskedastic extreme value model
allow for such correlations and are computationally becoming feasible due to
innovations in simulated maximum likelihood techniques and powerful computers.
Given these developments, it is important to utilize the appropriate choice model in
the indicator functions so as to create the correct “generalized residual” for the
control function or to create the precise instrument, if instrumental variable
23
approaches are used. Comparing these flexible choice models to the traditional
multinomial logit model approach will be one of the aims of this dissertation. The
proposed nesting structure for the treatments of RA is presented below in
Appendix A.
2.2 ECONOMETRICS LITERATURE ON SELECTION BIAS
2.2.1 Methods for Correcting Selection Bias
James Heckman's seminal work on sample selection bias (Heckman 1976,
1979), proposed a simple two-step procedure to overcome the misspecification in
making population inferences using estimates from a non-random sample. As
suggested by Heckman, (1976, 1979), the first step is to estimate the probability of
participation over the entire (N) observations by maximum likelihood probit and then
construct the estimate of the inverse Mills ratio (IMR). One can then consistently
estimate the parameters by ordinary least squares (OLS) over the subset of non-
random observations reporting values for the dependant variables, by including an
estimate of the inverse Mills ratio, as a regressor in the second step outcome model
(Heckman 1976, 1979). The two step procedure is straight forward, yet there are
issues with (1) adjusting standard errors in the second step to account for the first
step estimation, (2) identification of the selection equation either through the non-
linearity of the IMR or by employing an instrument variable which impacts the
probability of participation but not the outcome, and (3) violation of joint normality
assumption (Greene 2002). Leung and Yu provided conditions under which the
identification of parameters can be met in the Heckman two-step
24
procedure (Leung and Yu 1996). The main criticism of this two-step approach
however, is the assumption regarding joint normality of the two errors. A departure
from normality assumption leads to poor performance by this approach (Duncan
1983; Goldberger 1983). As an alternative to the bivariate normality assumption,
Olsen provided a technique with a linear probability model for the selection model
and derivation for a correction similar to the IMR. The advantage of Olsen's method
is that it only requires regression techniques so that an iterative probit is not a
necessary first step (Olsen 1980). Lee, introduced computationally simpler method to
generalize selectivity in the polychotomous outcomes where the error is not
restricted to be normally distributed (Lee 1983). The advantage of Lee’s methods is
that the approach is ready to be generalized to more complicated polychotomous
choice models, such as the alternate choice models proposed in this study.
Hay (1980) and Dubin and McFadden (1984) have also extended the
Heckman (1979) estimator to models with polychotomous outcomes and their
models are based on the use of a truncated conditional expectation function (Hay
1980; Dubin and McFadden 1984). Terza's generalization to polychotomous
selectivity maintains the assumption of joint normality among the errors (Terza
1985). Barrios, provides a generalized sample selection bias correction method under
every random utility maximization compatible specification for the selected sample
using a mixed logit selection equation. He considers a generalization of the Heckman
two stage estimator with a mixed logit specification in the first step (Barrios 2004).
Unlike others, Barrios, however, does not provide proofs of the consistency of his
25
estimator. Vella (1998) is a good survey of sample selection bias correction by
parametric and semi-parametric procedures (Vella 1998). Although, these techniques
mentioned above are meant for generalization based of subsample of positive valued
observations, Heckman’s (1978) paper developed a class of econometric models for
simultaneous equation systems with dummy endogenous variables (Heckman 1978).
The framework can be generalized to the polychotomous treatment dummy
endogenous variables case, such as the one observed in this study.
2.2.2 Applications of Sequential Decision, Polychotomous Choice and IIA
The econometrics literature on estimation of sequential decisions,
polychotomous choice and accounting for independence of irrelevant alternatives is
rich in the fields of labor and welfare economics. A partial list of relevant articles
includes the work of Abowd and Farber who have developed a model to account for
the sequential decision which leads to queuing for union status jobs (Abowd and
Farber 1982). They reject the simplified logit and probit models for sample selection
due to misspecification since, those models were not based on consistent behavioral
theory. Trost & Lee present a model with polychotomous choices and selectivity and
then apply it to the problem of estimating the returns to technical school training
(Trost & Lee 1984).
Gyourko and Tracy estimated a general selection model in which worker’s
selection across four labor markets was modeled by a multinomial logit selection
equation. They found evidence of positive selection bias in the private/nonunion
26
sector and of negative selection bias in the public/union sector (Gyourko and Tracy
1988). Vijverberg extended the work of Hay (1980) and Lee (1983) to include cases
where selectivity bias results from a two-stage choice with multiple alternatives. The
paper underscores the importance of modeling the two stage selectivity separately,
since, a single model may show lack of selectivity if the effects of the two
selectivities are in opposite direction (Vijverberg 1995). Vijverberg, suggests the
dual- λ method to account for this two-stage selectivity, since, in the presence of dual
selection criteria, estimation strategies that account for only one criterion still lead to
biased estimates. Lee, (1995) provided general formulas for the computation of
opportunity costs of unchosen alternatives in sample selection models with
polychotomous choices (Lee 1995).
Applications in healthcare field include, Gertler et al. study which corrects
for sample selection bias using a methodology derived in Dubin and McFadden
(1984). Their model required the estimation of a reduced form multinomial logit
model of provider choice, from which a set of Dubin-McFadden selection correction
terms were constructed for each individual. The predicted correction terms were
included as regressors in their hedonic price regression (Gertler et al. 1987). Haas-
Wilson et al. estimated the probability of beginning a certain type of mental health
treatment episode using a multinomial logit model; and secondly, analyzed the level
of outpatient utilization within episodes (Haas-Wilson et al. 1989). Dowd et al. had
proposed a model that corrects simultaneously for bias introduced by endogenous
health plan choice and a high proportion of the sample using no services. The
27
endogeneity in health plan choice was modeled by a multinomial logit model and
transformation into a standard normal random variable accomplished by the
procedure described in Lee (1983) (Dowd et al. 1991). Hylan et al. estimated the one
year direct cost for patients initiating any one of the TCA’s or SSRI’s using two
stage model based on the framework of Lee (1983) to correct for the non-random
sample (Hylan et al. 1998). Edgell et al. examined the economic outcomes associated
with initial treatment choice following a diagnosis of depression. They classified
patients into one of 4 treatment cohorts: no therapy, psychotherapy, drug therapy,
and combination therapy. Potential sample selection bias was accounted for by using
a 2-stage econometric estimation procedure where initial treatment choice was
estimated using a multinomial logistic regression model in the first stage, and total
and mental healthcare costs were estimated in ordinary least squares regression
models in the second stage. Log predicted costs from the second stage were
compared to determine the relative costs associated with each cohort (Edgell et al.
2000).
Nested Logit Model as Selection Equation
Falaris (1987) specifies a multiple choice migration model with selectivity
(Falaris 1987). He controls for the selectivity bias in choice of the state to which
person migrates and the resulting wage earned due to migration by a nested logit
model proposed by McFadden (1981) in conjunction with Lee's (1983) generalized
polychotomous choice model estimator to test for unobserved similarities. Falaris
(1988) specifies a two-period nested logit migration model with selectivity to
28
account for three methodological issues: (a) the presence of selectivity in wage
equations; (b) the existence of unobserved similarities between subsets of locations;
and (c) the effect of choices in one period on choices in subsequent periods (Falaris
1988). Controlling the effect of choices in period one on choices in the second period
was accomplished by specifying a recursive nested logit migration model, while
selectivity was controlled by Lee's (1983) approach.
Hoffman and Duncan estimated both a multinomial logit and a nested logit
model of the family structure and welfare use choices of divorced or separated
women in the years following the dissolution of their marriage. Their main interest
was in the effect of aid to families with dependent children (AFDC) benefits on the
probability of remarriage. They found the results of the two models to be
dramatically different in regards to the issue of AFDC benefits and the probability of
remarriage (Hoffman and Duncan 1988).
Applications of nested logit selection equation in healthcare field include;
Dor et al. study which estimated a nested multinomial logit model of provider choice
to investigate the role of travel time in rationing medical care services (Dor et al.
1987). Feldman et al. estimated a nested logit model for modeling health plan choice,
with freedom to choose doctor being the variable that distinguished health plan nests.
The nested logit model was chosen to account for independence of irrelevant
alternatives problem in the multinomial logit approach to model health plan choice
(Feldman et al. 1989). Spencer et al. investigated geographic variation in the
treatment of early stage prostate cancer by employing a 2-stage nested logit model to
29
compare surgery, radiation therapy and non-curative treatment among 4 geographic
regions of the United States (Spencer et al. 2004). Their statistical approach
accurately represents the clinical decision making involved with a new diagnosis of
prostate cancer, and is appropriate for a decision with the 3 non-independent options
since, it relaxes IIA assumption. The first stage of decision involves the physician,
who assesses whether the patient is a candidate for active treatment with radiation
and surgery, and in the second stage the patient decides between the treatments after
a full discussion of the risks and benefits of surgery and radiation (Spencer et al.
2004). Fortney et al. modeled the joint decision to seek depression treatment and
choice of provider sector (Fortney et al. 1998). They tested three discrete choice
specifications to model the joint decision; the sequential binary logit models, a
multinomial logit model, and a nested logit model and identified the nested logit
model as the preferred model specification based on a likelihood ratio test (Fortney
et al. 1998). Zhang et al. examined the net economic cost, defined as the sum of
changes in lost earnings and depression treatment costs, and found that the cost of
depression treatment was fully offset by savings from reduction in lost work days
(Zhang et al. 1999). To correct for the potential selection bias in treatment choice,
the probability of seeking treatment for depression was assessed by a nested logit
model and they used an instrumental variable which was the actual travel distances
to mental health providers and primary care providers as predictors for choice of
depression treatment (Zhang et al. 1999).
30
Selection Bias Literature in Rheumatoid Arthritis
Selection bias adjustment studies specific to arthritis have generally relied on
traditional Heckman (1976) type correction for accounting for non-random treatment
assignment. Mitchell and Butler compared two methods to control for the non-
random sample of arthritis patients, Heckman (1976) and Olsen (1980). They
reported that when selection bias was accounted for, the estimated absolute effects of
arthritis increased and the percentage of the gap between arthritic and non-arthritic
males explained by arthritis, as opposed to other factors, increased (Mitchell and
Butler 1986). MacDonald et al. reviewed the evidence for channeling/selection bias
among users of meloxicam and COX-2-specific inhibitors and discussed the impact
that this channeling may have on evaluation of the safety of these drugs compared
with the older, non-selective NSAIDs. The study employed propensity scores
method as adjustment for differences in multiple baseline characteristics
(MacDonald et al. 2003).
2.2.3 Note on Potential Outcomes Framework, Instrumental Variables,
Propensity Scores and Regression Discontinuity Designs
Widely-used cross-sectional estimators suffer from the defect of being
heavily reliant on distributional assumptions. However, Heckman and Robb (1985)
demonstrated that unless explicit distributional assumptions are invoked all cross-
section estimators require the presence of at least one regressor variable in the
decision rule determining selection of treatment (Heckman and Robb 1985). They
further argued that although this requirement may seem innocuous, but it rules out a
31
completely non-parametric cross-section approach (Heckman and Robb 1985). An
“exclusion restriction” (also called rank condition) defined as simultaneous omission
of a variable from the outcome equation and its inclusion in the selection equation is
necessary for identification in cases where explicit distributional assumptions are not
invoked (Heckman and Robb 1985; Cameron and Trivedi 2005). Furthermore they
also demonstrated that for most cross-sectional estimators this requires precise
specification of the treatment decision rule, while longitudinal and repeated cross-
section estimators do not require this exclusion restriction under certain assumptions.
Our study hypothesis argues for the case of the nested or mixed logit model as the
precise specification of the treatment decision rule.
The literature on estimating treatment effects based on the potential outcomes
model (Rubin 1976; Holland 1986) makes no distributional assumptions on the error
and are considered superior to conventional econometric structural framework which
is heavily dependent on what seem un-testable assumptions about the unobserved
error. However, in the potential outcomes framework, the only method to account for
selection on unobservable factors is to define an instrument variable which is
correlated (highly) with the treatment assignment but has no direct effect on the
outcome (Heckman et al. 2000). Furthermore, the instrument has to be orthogonal
(technically not needed if distributional assumptions are invoked) to the
unobservable selection bias. Defining or finding one or more instruments for
treatment assignment is the identifying condition necessary for estimation of the
various policy relevant treatment effects (Wooldridge 2002).
32
Heckman and Robb questioned the plausibility of these conventional
specifications based on counterfactuals since, they are not motivated by economic
theory and when examined in that light they seem implausible (Heckman and Robb
1985). Furthermore, given the Medi-Cal dataset, it is very difficult to define or find
an instrument which meets the above mentioned requirements, let alone finding one
that (a) accounts/controls for the IIA problem in treatment assignment, and (b) is
uncorrelated with the outcome. Although, the counterfactual setting allows some
leniency in misspecification of the maximum-likelihood selection estimator, still if
the correlation between instrument and the treatment is low, the IV estimator is
inefficient (Heckman 1995). Furthermore, even if we find a suitable instrument and
use an IV estimator under the counterfactual setting, it may only be able to estimate
the local average treatment effect (LATE). If there is presence of heterogeneity in
response to treatment, which is more likely the case when comparing most medical
treatments, the IV method breaks down in absence of the monotonicity assumption
(Angrist 2003). Heckman and Vytlacil, claimed that this monotonicity assumption is
strong and there is no guarantee that it will be satisfied (Heckman and Vytlacil
2005). LATE is a parameter which is generally calculated over an unobservable
population and is dependant over the defined instrument, so two researchers using
two different valid instruments on the same sample will come to different
conclusions (Wooldridge 2002; Heckman and Vytlacil 2005). Lastly, although using
an IV estimator may purge the endogeneity in treatment, it does not offer direct
means to test the endogeneity in treatment assignment.
33
Given the research objective, the study is also not amenable for sharp or
fuzzy Regression Discontinuity designs for evaluating treatment effects due to
(1) lack of an observed covariate based upon which a fixed threshold of treatment
assignment can be defined, (2) polychotomous treatment choice, and (3) inability to
explicitly test for endogeneity (Imbens and Lemieux 2007).
Lastly, propensity scores cannot remove hidden biases when treatment
selection is based on unobservable factors, except to the extent that unmeasured
prognostic variables are correlated with the measured covariates used to compute the
propensity score (Rosenbaum and Rubin 1984; Braitman et al. 2002; Austin et al.
2005; and Stukel et al. 2007). In the current analysis, treatment choice factors
causing non-random selection of drug treatment are unobserved to the analyst along
with self selection due to idiosyncratic gains by patients. Given these facts,
propensity score technique cannot be used to control for the endogeneity in treatment
and heterogeneous treatment effects. We will have to rely on parametric
generalizations of sample selection techniques, such as the one developed by Lee
(1982) to estimate treatment effects, in the current study.
Lee’s Method for Selectivity Correction-
The reason for employing the nested and mixed logit to model selectivity in
this study is because the selectivity bias terms in the regression equation may be
sensitive to the specific probability models even though there may be only slight
differences in the probability models themselves (Lee 1982). Lee’s approach
provides a way to generate a large class of models with selectivity. By specifying
34
different transformations, we can allow different implicit distributions on the error
and thus, any specific probability choice model need not dictate the method of
correcting the selectivity bias term (Lee 1982).
Lee's method has two advantages over the other polychotomous (two-stage)
methods discussed earlier. First, Lee's method allows for full-information maximum
likelihood (FIML) estimation, while the other methods are two-stage methods in
which the discrete choice model is estimated first and then the continuous choice
model is estimated using one of several methods to account for selectivity bias. Thus,
Lee's method facilitates asymptotically more efficient estimates in the
discrete/continuous choice model if FIML is employed. Second, the expressions for
the asymptotic covariance matrices of the two-stage estimates are very complicated,
while the asymptotic covariance matrix in Lee's method can be obtained directly
from the maximum likelihood estimation (FIML). Lee's method is also very flexible
and can accommodate any model formulation for the discrete choice decision with
little change in the methodology (Bhat 1987). Schmertmann, however, warned that
Lee’s approach requires strong implicit restrictions on covariance between outcomes
and selection indices. The author's Monte Carlo study demonstrated that the Lee
estimator exhibits significant bias when the data-generating process does not
conform to its implicit covariance assumptions (Schmertmann 1994).
2.2.4 Characteristics of Cost/Expenditure Data
Cost data generally has nonnegative values, high zero mass,
heteroskedasticity, heavy skewness in the right tail, and is leptokurtic. These
35
characteristics of cost data are against the requirements of OLS estimation to be the
best linear unbiased estimator (BLUE). Although, OLS may be unbiased if there is
no zero mass problem, inferences based on the OLS estimates are in general, biased
due to the above data characteristics. Many studies have shown the consequences of
ignoring these characteristics of cost data by comparing commonly used techniques
to account for these issues and have suggested improved estimators (Duan 1983;
Duan et al. 1983; Hay and Olsen 1984; Manning 1998; Mullahy 1998; Blough,
Madden, and Hornbrook 1999; Ai and Norton 2000; Manning and Mullahy 2001;
Basu et al. 2004; Buntin and Zaslavsky 2004; Manning et al. 2005; and Basu, and
Rathouz 2005). Manning and Mullahy, (2001) provided a straightforward algorithm
for choosing amongst the alternative estimators (Manning and Mullahy 2001).
Manning, (2006) is a good review of the various techniques used to model cost data
(Manning 2006).
Methods that take the special feature of cost data are needed to get an
unbiased estimate of treatment effects. One of the most frequently used models for
health care cost utilizes the log-link relationship to describe the relationship between
Ln(E(Y|X)) = X’ β, or E(Y|X) = exp(X’ β) where ‘Y’ is cost outcome and ‘X’ is
covariate vector. In the exponential conditional model (ECM), the link function
directly typifies how the expectation on the raw scale is related to the predictors.
The direct interpretation as being a multiplicative effect of the linear predictor on
total health care costs is another advantage of the log-link function. Thus,
retransforming the results from the log to the raw scale is unnecessary. Secondly,
36
zero values observed frequently in the cost data are adeptly handled with this
generalized linear model (GLM) model and hence, it can be estimated on the entire
sample, if not, it can also be used as the second part of a two-part model (Manning &
Mullahy 2001; Buntin & Zaslavsky 2004). Even more generalized methods as
compared to ECM for expenditure modeling are the generalized gamma distribution
model (GGM) (Manning et al. 2005) and Extended Estimating Equations (EEE) in
GLM (Basu and Rathouz 2005).
Generalized gamma is appealing in this context because it includes several of
the standard alternatives as special cases – OLS with a normal error, OLS for the log
normal, the standard gamma and exponential with a log link, and the Weibull
(Manning et al. 2005). EEE in GLM is an extension to the estimating equations in
generalized linear models to estimate parameters in the link function and variance
structure simultaneously with regression coefficients (Basu and Rathouz 2005). In
these extensions to GLM proposed by Basu and Rathouz, rather than focusing on the
regression coefficients, the purpose of their models is inference about the mean of
the outcome as a function of a set of covariates, and various functionals of the mean
function used to measure the effects of the covariates. The proposed estimation
method not only helps to identify an appropriate link function and to suggest an
underlying distribution for a specific application but also serves as a robust estimator
when no specific distribution for the outcome measure can be identified (Basu and
Rathouz 2005).
37
In the current study, we cannot use any of these sophisticated techniques to
account for the peculiarities in the expenditure data. The reason is that the
endogeneity correction using two step approaches use variants of the inverse Mills
ratio (IMR) in the outcome equation as a selection bias correction term. The outcome
equation which includes the selection bias correction term is only identified in a
linear model specification. Most of these models such as GLM, ECM, GGM, and
EEE typically involve a multiplicative specification as opposed to a linear
specification, thus, are incompatible for combining with the IMR type endogeneity
correction term. Secondly, given the panel data available for analysis in this study,
extensions of these models essentially through generalized estimating equations
(GEE) requires stronger independence assumptions as compared to the less strict
contemporaneous correlations assumption afforded by fixed effects approach. Lastly,
there are no diagnostic or constructive tests such as Park’s, Hosmer-Lemeshov test
available for model selection and specification in panel data setting. Hence, the only
options available are to log the cost data and specify a log-linear model and
retransform using smearing estimator or to employ OLS ignoring the skewness in the
data distribution. Log transformation to addresses skewness in expenditure data is
appealing and popular since, it pulls in the right tail of the distribution much faster
than the left tail. However, it also creates many complications during
retransformation especially when heteroskedasticity is involved.
38
If multiple heteroskedastic covariates are involved, each of them needs a unique
smearing estimator, in other words we need to know the form of the
heteroskedasticity (Duan 1983).
The model studied in this dissertation allows for unobserved
heteroskedasticity (referred to as unobserved heterogeneity) and hence, it’s not
possible to obtain unbiased estimates if log transformation is performed on the
outcome variable. Another problem with using smearing retransformation is the
reintroduction of covariate imbalance during retransformation. This necessitates the
application of recycled prediction technique to avoid reintroduction of covariate
imbalance. Although one could work out the logistic of using recycled prediction
technique in presence of multiple treatments, the process of bootstrapping to recover
standard errors complicates this approach. Conceptualizing the combination of the
dual bootstraps needed, one for the 2
nd
stage outcome model and one for the recycled
prediction technique, is beyond the scope of this study. Lastly, since, we are dealing
with panel data, autocorrelation also needs to be factored in during the
retransformation. For all these reasons mentioned above, it is deemed best to use raw
scale expenditure and not perform log transformation on the dependant variable.
The estimators developed by Mullahy (1997) and Terza (1999), which can
account for the non-linear specification of the outcome equation, need presence of
valid instrument and/or non-standard statistical software for estimation and hence,
are not considered for this study (Mullahy 1997; Terza 1999).
39
2.3 A CONCEPTUAL MODEL FOR EVALUATION OF TREATMENT
EFFECT
According to Heckman and Robb, two different definitions are associated
with the notion of a selection bias free estimate of the impact of treatment on the
outcome which is total quarterly healthcare expenditure (Heckman and Robb 1985).
The first notion defines the structural parameter of interest as the impact of treatment
on quarterly expenditure if RA patients are randomly assigned to biologic DMARDs,
also known as the average treatment effect (ATE) (Heckman and Robb 1985).
The second notion defines the structural parameter of interest in terms of the
difference between the post-treatment expenditure of those treated with biologic
DMARDs and what the expenditure in post-treatment years for these same patients
would have been in the absence of treatment, also known as the average treatment
effect in the treated (ATET) (Heckman and Robb 1985). These two notions come to
the same thing only when treatment has an equal impact on everyone (homogeneous
treatment effect) or else if assignment to treatment is random and attention centers on
estimating the mean response to treatment (Heckman and Robb 1985). The second
notion, ATET, is most useful for forecasting future treatment effects when the same
treatment assignment rules which have been used in available samples, characterizes
future treatment (Heckman and Robb 1985). The answer to this question is all that is
required to estimate the future treatment effect if future selection criteria are like past
criteria (Heckman and Robb 1985). Defining ATET in presence of multiple
endogenous treatments and heterogeneous treatment effects is extremely complicated
40
and hence, we restrict estimation of ATET only under the assumption of
homogeneous treatment effect.
For estimating ATE, we propose panel data endogeneity corrected models for
estimating treatment effects. Unlike the case of ATET, we do not impose the
restrictive assumption of homogeneous treatment effects. We allow for the fact that
individual response to treatment can deviate from the mean and that these
idiosyncrasies are correlated to treatment choice. In other words, if the treatment
effect varies in the population even after controlling for all the observed covariates,
there is a distribution of responses that cannot in general be summarized by a single
number (Heckman et al. 2006). Even if we are interested in the mean of the
distribution, a new phenomenon distinct from selection bias/endogeneity might arise.
This phenomenon can be appreciated in the current analysis where the physician who
acts as an agent for the patient may prescribe a certain treatment because of the belief
that particular patient may have an enhanced (above average) response to that
particular treatment. Heckman et al. (2006) defines this as the problem of “sorting on
the gain” and such models of to be models with “essential heterogeneity”. The
application of instrumental variables to this case is more problematic. In the binary
treatment case, the parameter identified is the “local” average treatment effect, which
generally is limited in scope since, it varies based on the employed instrument.
Furthermore, in case of models with essential heterogeneity and
polychotomous discrete treatment choice, the misspecification of the indicator
function (either its functional form or its arguments) in general produces biased
41
estimates of the parameters of the model under the control function as well as the IV
approaches (Heckman et al. 2006). Moreover, for the polychotomous choice, IV
based estimation requires a unique (non-overlapping) instrument/exclusion
restriction for each treatment choice (Heckman et al. 2006). For the current study,
this is the reason why all the “standard” DMARDs had to be pooled in a single group
as a unique exclusion criteria for each of them is not available in the Medi-Cal
dataset.
In the model with essential heterogeneity, the specification of the
choice/selection equation affects the interpretation of any IV estimator. This feature
is absent in the classical model where specification of the full instrument list and
choice model is irrelevant to the interpretation of what IV estimates. Under
heterogeneity, two economists using the same valid instrument and the same
outcome equations but maintaining different models of economic choice will
interpret the same point estimate differently. So will two economists using the same
instrument and the same explanatory variables (Z) in selection model but using
distributions of Z that are different. The agnostic and robust features of IV in its
classical setting disappear in a model with essential heterogeneity (Heckman et al.
2006). This brings us to the second objective of the study which is to understand the
impact of the selection/choice model’s functional form on the estimated treatment
effect. In particular, we will model the selection equation by multinomial, nested,
and mixed logit specification and analyze the resulting estimate of ATE.
42
Traditional fixed effects panel data endogeneity corrected model allows for
time invariant heterogeneity to be correlated to the error, in the form of individual
intercepts. However, it treats heterogeneity as a nuisance parameter (Heckman and
Robb 1985; Wooldridge 2002; Hsiao 2003; Cameron and Trivedi 2005). ATE
parameter is thus identifiable since, we purge the heterogeneity if it manifests only as
time invariant intercept effects. A more realistic model is to allow for individual
slopes which in turn are correlated to the endogenous treatment and hence, to the
error. This model was first introduced by Heckman and Vytlacil as a “correlated
random coefficient” (CRC) model (Heckman and Vytlacil 1998). Due to the
generality afforded by this model, we use this model as our framework and extend it
to the case of multiple treatments which appear endogenously in the model.
Thus, we will be estimating heterogeneous (ATE) and homogeneous (ATE1)
average treatment effect (average treatment effect in the treated (ATET) is equal to
ATE under the homogeneity assumption) of biologic DMARDs in this study while
controlling for unobservable factors contributing to the endogeneity in the outcome
model. Differences in ATE1 and ATE estimates will reject the homogeneity of
treatment effects assumption since, in absence of heterogeneity, and after controlling
for selection bias, ATE is equal to ATE1.
Motivating the Problem
Suppose a policy is proposed for formulary expansion of biologic DMARDs,
i.e. move patients currently on standard DMARDs to biologics DMARDs. These
drugs have been tried in some patients and we know their outcomes (quarterly total
43
expenditure). We also know outcomes in patients where biologic treatment was not
adopted. What can we conclude about the likely effectiveness of this policy in
patients who are not on the biologic therapy?
To answer this question, we build a model of counterfactuals. Let Y
0
be the
outcome of a patient under a standard DMARD. Y
1
is the outcome if the policy is
implemented. Then (Y
1
− Y
0
) is the treatment effect of the policy. It may vary
amongst patients. We observe characteristics S of various patients. It is convenient to
decompose Y
1
into its mean given S, μ
1
(S), and deviation from mean, U
1
. We can
make a similar decomposition for Y
0
:
Y
1
= μ
1
(S) + U
1
Y
0
= μ
0
(S) + U
0
….……..(1)
It may happen that after controlling for the vector (S), (Y
1
− Y
0
) is same for
all patients. This is the case of homogenous treatment effects given S. However, it is
more likely that patients vary in their response to the policy even after controlling for
the covariate vector (S).
It may be the case that after controlling for (S), treatment effects are
heterogeneous but, if treatment decisions are not made based on these heterogeneous
outcomes then we can use conventional instrumental variable (IV) and control
function approaches. However, if treatment decisions are made based on the
unobserved heterogeneity, then it’s correlated to the treatment indicator and the
model is termed as model with essential heterogeneity (Heckman et al. 2006).
Instrumental variables methods fail in such framework and in the binary case the
44
parameter identified is “local” ATE (instrument specific and over undefined
population) (Heckman et al. 2006). Heckman et al. came up with local instrumental
variable (LIV) approach to counter this problem in a marginal treatment effects
(MTE) framework (Heckman et al. 2006). We extend their framework to multiple
treatment case but, using the correlated random coefficient model. The correlated
random coefficient model is the focus of a large literature in microeconometrics and
labor economics (Heckman et al. 2006). For person i, it writes outcome Y
i
in terms
of choice indicator D
i
. D
i
= 1 if a choice is made; D
i
= 0 if not. Keeping regressors S
i
implicit, the outcome equation is
Y
i
= α
i
+ β
i
D
i
….……..(2)
where, the causal effect of D
i
on Y
i
, varies among individuals and is
correlated with D
i
. As described in Heckman et al. (2006), this model is a version of
the generalized Roy model (Roy 1951). Assuming that E( β
i
) if finite, so E( β
i
) = β
bar
or mean of β is well defined, most recent studies focus on estimating means or
quantiles of the distribution of β
i
(Heckman et al. 2006). The conventional model
that motivated previous research assumed β
i
= β (i.e. no response heterogeneity). The
CRC model assumes β
i
has a non-degenerate distribution, moreover
Cov (D
i
, β
i
) ≠ 0 ….…….(3)
and
Cov (D
i
, α
i
) ≠ 0 ……….(4)
When (3) holds, marginal returns differ from average returns. Instrumental
variables applied to (2) when (3) holds produces an instrument-dependent parameter.
45
Different instruments estimate different parameters. In general, IV based on an
instrument Z, does not estimate E( β
i
). Under conditions specified in Imbens and
Angrist (1994) and Heckman, Urzua, and Vytlacil (2006), IV estimates weighted
averages of the marginal effects.
If we assume separability between the observable and unobservable
confounders, the model for potential outcomes conditioned on covariates vector, S,
and instruments, Z, (both implicit below) is
Y = μ
0
+ ( μ
1
− μ
0
+ U
1
− U
0
)D
i
+ U
0
……….(5)
In this model, covariance (D, U
0
) ≠ 0 is the selection/endogeneity bias while
covariance (D, β| S, Z) ≠ 0, is the selection on the gain or heterogeneity bias. This
phenomenon can be appreciated in the current analysis where the physician who acts
as an agent for the patient may prescribe a certain treatment because of the belief that
particular patient may have an enhanced (above average) response to that particular
treatment. Since, we are adapting switching regression model which allows full
parameter heterogeneity, into a pooled treatment effects model, hence, these two
sources of bias have to be dealt simultaneously. In such cases, estimates of the
treatment parameters can be obtained by assuming the marginal treatment effects
(MTE) framework formally developed in the next section.
Marginal Treatment Effects Conceptual Model
In the current analysis, the treatment (C) can take on more than two values
i.e. treatment is polychotomous (see Appendix B for all the treatment alternatives)
C ∈ {c
1
, c
2
, . . . , c
M
}……………………..……….(6)
46
We want to define potential outcomes for every possible treatment value at time (t)
Y(c
mt
), c
m
∈ C……………………………………..(7)
One way to define treatment effects is to make pair wise comparisons of the form:
Δ
mt,nt
= E[Y(c
mt
) − Y(c
nt
)], c
m
, c
n
∈ C . ….………..(8)
However, we only observe the potential outcome corresponding to the
treatment actually obtained.
To formalize this, let
D(c
mt
)
=
= =
Otherwise 0
c C iff 1
mt
..……………….…….……..(9)
we can define the observed outcome as
Y =
==
M
1 m
mt mt
T
1 t
) )D(c Y(c …………….………....……….(10)
If the treatment is independent of the potential outcomes, so that
c
mt
⊥ {Y (c
mt
)}, c
m
∈C
, ..……………….…..…………….(11)
then E[Y(c
mt
)] = E[Y | D(c
mt
) = 1]
However, this is a very strong assumption and never supported in
observational studies due to selection bias in treatment assignment caused by
observable and unobservable factors. As seen from the literature, patient’s
willingness or aversion to various medication delivery systems, contraindications,
co-morbidities, concomitant medications, susceptibility to infection, logistics, and
other factors which are unique for each patient such as preferences regarding the
treatment options, route and frequency of drug administration and financial
47
considerations of treatment along with the recommended treatment guidelines in
existence are mostly unobservable (to the analyst) factors contributing to treatment
assignment and causing endogeneity in treatment selection. Under the potential
outcomes framework, endogeneity is addressed by instrumental variables approach.
However, if treatment effect is not homogeneous, then assumption of consistency in
IV breaks down and for binary treatment the treatment parameter identified is the
LATE. LATE and Local instrument variables (LIV) do not have straightforward
extensions to the case of multiple treatments which are the focus of this study.
In such cases, estimates of the treatment parameters can be obtained by
assuming the marginal treatment effects (MTE) framework. The MTE framework
employs a latent index for treatment selection and thus using the output from a two-
step procedure we can estimate the ATE. To motivate the justification for the
selection bias correction term, we define a traditional structural model as follows:
The decision to undertake treatment may be determined by the patient (i) at
time (t) or by the physician or both. Whatever the specific content of the rule, it can
be described in terms of an index function framework. Let I
it
, be an index of benefits
to the appropriate decision-maker from treatment. It is a function of observed (Z
it
)
and unobserved (V
it
) variables. Thus,
I
it
= Z
it
+ V
it
………………….…………………….……….(12)
In terms of this function, redefine equation (4) as
D(c
mt
)
=
> =
Otherwise 0
0 I if 1 it
…...….………...…………..….…..…(13)
48
Letting I
it
denote the index function in decision rule and further assuming that Z
it
is
distributed independently of V
it
(V
it
is assumed to have zero mean and variance σ
1
2
),
makes equation (12) a standard discrete choice model which is in general consistent
with the random utility model.
Under the random utility theory, the random utility function of individual ‘i'
for choice ‘j’ at time ‘t’, is decomposed into a deterministic and stochastic
components
U
ijt
= Z
ijt
+ ε
ijt
…...…………...……………….…………(14)
where Z
ijt
is a deterministic utility function, assumed to be linear in the
explanatory variables, and ε
ijt
is an unobserved random variable. Different
assumptions on the distribution of the error components gives rise to different classes
of models and are concisely listed in Table 2.2
Table 2.2 Types of Discrete Choice Models and their Error Distributions
Model Type Utility Function Distribution of ε
ij
Multinomial Logit U
ijt
= Z’
ijt
β + ε
ijt
IEV independent and identical
Nested Logit U
ijt
= Z’
ijt
β + ε
ijt
GEV correlated and identical
Mixed Logit U
ijt
= Z’
ijt
β + ξ
ijt
+ ε
ijt
IEV independent and identical
Heteroskedastic
Extreme Value
U
ijt
= Z’
ijt
β + ε
ijt
HEV independent and non-
identical
Multinomial Probit U
ijt
= Z’
ijt
β + ε
ijt
MVN correlated and non-
identical
(IEV stands for type I Extreme Value (or log-Weibull) distribution; HEV stands for
Heteroskedastic Extreme Value distribution; GEV stands for Generalized Extreme Value
distribution; MVN represents Multivariate Normal distribution; and ξ
ij
is an error component)
(source: SAS MDC Procedure Reference- SAS Institute Inc. 2008)
The utility function in the multinomial discrete choice models, is assumed to
be linear, so that U
ijt
= Z’
ijt
β. The multinomial probit model is derived when the error
disturbances, ε
ijt
, have non-identical and non-independent normal distribution. In
49
case of the multinomial logit models, the error disturbances have independent type I
extreme value distribution function, exp(-exp(- ε
ijt
)) also known as the Gumbel
distribution. When the random components have identical and non-independent
Gumbel distribution it gives rise to the nested logit model. The more flexible
heteroskedastic extreme value (HEV) model assumes non-identical and independent
distribution of the error disturbance. A multinomial probit model requires arduous
computation compared to the family of multinomial choice models derived from the
extreme value distributed utility function. The main reason for this is the multi-
dimensional integration in the estimation of the multinomial probit. In addition, a
multinomial probit model requires more parameters than other multinomial choice
models. As a result, multinomial and nested logit models are used more frequently
even though they are derived from a utility function whose random component is
more restrictively defined than the multinomial probit model (SAS Institute Inc.
2008).
In the current study, the hypothesized discrete choice model is the nested and
mixed logit model, which is consistent with random utility theory and correctly
specifies the treatment selection decision while controlling for IIA problem (See
Appendix A for the nesting structure). The mixed logit can be specified as an error
components model or as a random parameters model, for the purpose of this study,
since, we are just interested in controlling for the correlations of treatment choice, we
specify the mixed logit model as an error components mixed logit model.
Specifically, binary exogenous variables were assumed to have uniform error
50
components while continuous exogenous variables assumed to have normal
distribution of error components.
Hypothesis testing of appropriate model choice can be undertaken by
comparing a multinomial choice model to the nested and mixed logit model by
Hausman test, and also Wald, Lagrange Multiplier and Likelihood ratio tests since,
the former model is a specialization of the later.
Due to the discrete nature of selection choice, the standard IV assumption of
conditional homoskedasticity of covariance breaks down especially, since, we allow
for heterogeneous treatment effects (Heckman et al. 2006). Since, the IV technique is
infeasible, we generalize the correlated random coefficients model to allow for
multiple treatments and also allow endogeneity in treatment assignment in a panel
data setting using control function approach. We will create a control function or a
generalized residual function to control for the endogeneity in treatment assignment.
The control function/generalized residual has to account for the polychotomous
discrete nature of the treatment selection equation (equation. 12 above) and hence,
standard control function needs to be modified. Lastly, since, the errors of the
selection equation follow an extreme value distribution which generally does not
overlap much with the multivariate normal distribution; transformations of the
extreme value error are needed to satisfy the joint normality of the structural errors
assumption which is invoked. To address this last issue we will apply Lee's
generalization for polychotomous choice models to handle selectivity/endogeneity in
the outcome equation. Thus, the choice model will have multinomial logit, the
51
nested, and mixed logit specifications (McFadden 1981), and we will apply Lee’s
(1983) technique based on order statistics to create the selection bias correction term
for the outcome equation (Lee 1983).
For the current study, the model of interest is a correlated random coefficients
model introduced by Heckman and Vytlacil and expanded to panel data by
Wooldridge (Heckman and Vytlacil 1998; and Wooldridge 2005). This approach
allows for heterogeneity in treatment effects in a panel data setting as follows-
For a random draw i from the population, the model is
Y
it
= W
t
a
i
+ X
it
b
i
+ U
it
, t = 1,...,T ……...…………….…………(15)
where Y
it
is the dependent variable i.e. the total quarterly expenditure, W
t
is a
1 x J vector of aggregate time variables, which we treat as nonrandom (specifically
for current study W
t
= 1 since, we do not expect rheumatoid arthritis patients treated
with DMARDs to improve over time), a
i
is a J x 1 vector of individual-specific
slopes on the aggregate variables, X
it
is a 1 x K vector of endogenous covariates that
change across time, b
i
is a K x 1 vector of individual-specific slopes, and U
it
is an
idiosyncratic error.
Equation (15) is a correlated random coefficients model because the
individual specific slopes, b
i
(as well as the elements in a
i
), are not assumed to be
mean independent of the endogenous X
it
. Wooldridge (2005) studied the consistency
of fixed effects estimators that sweep out the a
i
,
but act as if b
i
= β for all i.
Wooldridge’s key result and the extension here are as follows,
write b
i
= β + d
i
, and substitute into (15):
52
Y
it
= W
t
a
i
+ X
it
β + (X
it
d
i
+ U
it
) .....………….….………(16)
= W
t
a
i
+ X
it
β + V
it
..…..……....…………….………(17)
where V
it
= X
it
d
i
+ U
it
When we generalize this model to allow for heterogeneity in treatment effects
(i.e. individual correlated slopes b
i
) and multiple endogenous treatments, the
estimation gets extremely complicated but also more realistic to what we may
observe at the patient’s treatment effect level. From equation (17), we can easily see
that the individual heterogeneity (b
i
) is correlated with the model’s error. Now
assume that Z
1it
is a vector of strictly exogenous variables. Specifically, Z
1it
is a strict
subset of Z
it
from equation (12) which is the selection equation. Hence, we allow for
the exclusion conditions necessary for identification and do not have to rely on just
the joint normality distributional assumption for identification.
Thus, there are two kinds of potential omitted variables. We allow the
heterogeneity, bi, to be correlated with the endogenous X
it
and the exogenous Z
1it.
The time-varying omitted variable(s) is uncorrelated with Z
1it
– strict exogeneity –
but may be correlated with X
it
.
To put things in perspective, X
it
includes the multiple
endogenous treatment
indicators for treatment choice and Z
1it
are the demographic
and other exogenous covariates. This type of model is rarely studied in literature and
the generalizations are restricted to binary treatment case in balanced panels
(Murtazashvili and Wooldridge 2005). We do not restrict our study for balanced
panels and indeed the final fixed effects estimation is on an unbalanced panel.
53
To extend this model to multiple endogenous treatments and heterogeneous
treatment effects in unbalanced panel data framework, we make much stronger
assumption, namely strict exogeneity assumption conditional on (a
i
,b
i
):
E(U
it
|X
i1
,...,X
iT
, a
i
, b
i
) = 0, t = 1,...,T ….……..…………….…… (18)
We will further assume that the marginal distributions of U
it
, are
normal N(0, σ
2
2
) distributed, and also joint normality of the structural error U
it
from
equation (15) and V
it
from equation (12). Then we can proceed as explained
previously via a two step estimation strategy.
In the first step, we estimate equation (12), comparing between three models
namely multinomial, nested, and mixed logit. These discrete choice models are
estimated as pooled models since, fixed effects estimators of some panel data
discrete choice models may not be defined (due to incidental parameters problem)
and since, these complex models are not extensively studied in a panel framework
not much is known about such estimators. Secondly, as pointed by Fernandez-Val
and Vella (2007), estimation of a fixed effects selection equation will generally be
plagued by the incidental parameters problem and secondly the individual fixed
effects if controlled by dummies will create a bias in the control function used in the
second stage outcome equation, unless large T-bias correction is employed
(Fernandez-Val and Vella 2007). In view of the same we employ pooled discrete
choice models as mentioned above. Next, we obtain the predicted probabilities from
each model and construct the selection bias correction term ( λ
ijt
) for each treatment j
using the formulas provided by Lee 1983,
54
λ
ijt
= {- φ(J(P
ijt
))/P
ijt
}…………………………………………(19)
where J(P
ijt
) = Φ
-1
(P
ijt
) involves the inverse of the standard normal distribution.
φ is the standard normal probability density function and P
ijt
is the predicted
probability for individual i for treatment choice j and time t.
In the second step, we employ a fixed effects regression of
E[Y
it
|Z
1it
, X
it
] = η
i
+ Z
1it
γ + X
ijt
α
j
+ X
ijt
*(Z
1it
- Ż
i
) ζ
j
+ (h( λ
ijt
)) ρ + X
ijt
*((h( λ
ijt
))) ξ
j
....(20)
where Ż
i
is the expected value of Z
1it
and thus (Z
1it
- Ż
i
) is the individual
de-meaned (subtracted from the mean) exogenous variables vector, however, we
exclude the time dummies from the list of Z
1it
during the demeaning of these
exogenous variables. This de-meaning of the exogenous variables is analogous to the
with-in transformation of the fixed effects estimator. The last two terms are the
generalized residual function and the interaction of the generalized residual with the
endogenous treatment indicators respectively, with (h(λ
ijt
)) defined as
h( λ
ijt
) = {X
m
*( λ
imt
) - X
n
*( λ
int
)} ……………………………..…(21)
where m ≠ n are the j treatment options and λ
ijt
as defined in
equation (19). These
results are generalized from those given in Wooldridge (2002), Murtazashvili and
Wooldridge (2005), Heckman et al. (2006), Imbens & Wooldridge (2007) and
Fernandez-Val & Vella (2007).
In the correlated random coefficients model estimated as in equation (20) de-
meaning the exogenous variables and interacting with the endogenous regressor
assures that α
j
is the
estimated average treatment effect of treatment j compared to
baseline treatment (we describe this as standard DMARD treatment). The addition of
55
the generalized residual described in equation (21) controls for the time varying
endogeneity in treatment choice and interaction of the generalized residual with the
endogenous treatment allows for the correlated random coefficients. The
bootstrapped standard error on the generalized residual function is a valid test for
endogeneity of the treatment choice. Using estimated values for λ
ijt
creates
heteroskedastic errors and even otherwise since, we are dealing with generated
regressors due to the two-step procedure and de-meaning exogenous variables by
sample average estimates instead of population expectation values, the standard
errors are invalid. To avoid all these issues we bootstrap the errors accounting for the
panel nature of the data to get asymptotically consistent standard errors. The model
in equation (20) if estimated without the interaction terms assumes that the treatment
effect is homogeneous; this assumption may not be valid in medical treatments
where decision regarding therapy may be based on idiosyncratic gains/losses of
individual patients.
Study Hypothesis-
Failure to account for the endogeneity in treatment selection, may lead to
comparison of a sicker patient who is using biologic DMARDs to a healthier patient
who is using standard DMARDs. Empirical evidence for this hypothesis is supported
in a study by Grijalva et al. who had reported that new users of biologic DMARDs
used ambulatory services and selected medications more frequently than users of
traditional DMARDs, suggesting more severe or difficult to control disease activity
in these patients (Grijalva et al. 2007). They also claimed that poorly controlled
56
disease could result in additional comorbidities in these patients (Grijalva et al.
2007).
Invariably, by ignoring the decision process to administer biologic DMARDs,
the results will be biased in favor of standard DMARDs. Thus, the study
hypothesizes a positive selection bias introduced by endogeneity and correction for
this endogeneity should see a decrease (compared to naïve Random effects and Fixed
effects panel data models) in the incremental quarterly total expenditure in biologic
DMARDS as compared to standard and combination DMARDs.
Secondly, by ignoring sorting on gains or treatment heterogeneity, we are
over looking the possibility that those who select into treatment are more likely to
benefit from it. Assuming homogeneous treatment effect does not describe the true
data generating procedure and thus provides biased estimates. Lastly, ignoring the
model specification of treatment choice generation is a third source of error which
can impact the treatment effect parameter.
Hypothesis Statements-
1. The study hypothesizes a positive selection bias introduced by endogeneity
and correction for this endogeneity should see a decrease in the incremental
quarterly total expenditure in biologic DMARDS as compared to standard
and combination DMARDs
2. Comparing the endogeneity corrected incremental quarterly total expenditure
between the standard and biologic DMARDs, the incremental expenditure of
biologic DMARDs will be different when a nested/mixed logit selection
57
equation is specified, as compared to the incremental expenditure obtained
from a multinomial logit selection equation.
3. The multinomial logit selection equation will be rejected in favor of the
nested/mixed logit model, based on goodness of fit test since, the multinomial
logit is restrictive in assumptions and leads to IIA problems.
58
Chapter 3
Study Design and Methods
This chapter will describe the data, patient sample selection criteria,
construction of study variables, study design and methodology of this study.
We estimated the treatment effects on rheumatoid arthritis patients’ quarterly
total health care costs when adding biologic DMARDs to the drug therapy while
controlling the endogeneity in treatment choice and allowing for heterogeneity in
treatment effects. The structural parameters of interest in this study were the
heterogeneous average treatment effect (ATE) and the homogeneous average
treatment effect (ATE1). Average treatment effect was defined as the impact of
treatment on quarterly expenditure if RA patients are randomly assigned to biologic
DMARDs.
Study Perspective
This study was from the perspective of the third party payer i.e. Medi-Cal,
assessing the quarterly incremental expenditure associated with biologic DMARDs
in RA treatment.
3.1 DATA
This study used 100% of the fee-for-service portion of the California
Medicaid program (Medi-Cal) paid claims and eligibility files for Medi-Cal enrollees
from January 1st, 1999 to December 31st, 2005, to examine the above defined
treatment effects. Preliminary results indicated that biologic DMARDs use in the
59
Medi-Cal sample was first found in the year 1999 and hence, we used this year as the
baseline. Due to the Medicare modernization act, the payment/reimbursement system
has changed significantly since, January 1
st
2006, hence, to maintain a homogeneous
reimbursement environment, we restrict our analysis to December of 2005.
Medi-Cal covers outpatient care, inpatient, and prescription drugs for the
poor and disabled California residents. Medi-Cal paid claims files included
information from institutional claims at the claim level, professional services claims
at service level, and pharmacy claims at specific drug level. Service claims included
date of service, type of service, place of service, paid amount, billed amount, units
(days) of service, provider ID, primary and secondary diagnosis codes. Pharmacy
claims included NDC, fill date, days of supply, paid amount, billed amount, and
quantity. Eligibility files include the enrollment status of each month, in addition to
enrollee’s demographic information.
3.2 PATIENT SAMPLE
For estimating the treatment effect of biologic DMARDs on quarterly total
expenditure, we followed patients from similar start points of their rheumatoid
arthritis disease history. Any enrollee with diagnosis code for RA and filling a
prescription for biologic or traditional DMARDs and above the age of 18 years was
eligible. The diagnosis of RA was identified using ICD-9 code for RA 714.0-714.8
as given in Appendix D. This combination approach of selecting patients with an
ICD-9 code and prescription fill for DMARD had 85% sensitivity, 83% specificity
60
and 81% positive predictive value to identify RA patients, when using insurance
claims in combination with pharmacy data (Singh et al. 2004).
Patients included in this study were adult RA patients who were incidence
cases to DMARD treatments based on prescription medications usage. For each
patient, a “first-index date” was defined as the first date that a RA patient filled any
DMARD prescription. “Incidence case” of anti-rheumatoid medication, was defined
as, the patient with at least a twelve-month washout period prior to the “first-index
date”. This twelve-month washout period required every patient to have a minimum
12-month eligibility period without any DMARD medication prescription during that
period. Patients were excluded if they had less than 12 Medicaid-enrolled months
prior to the “first-index date”. To ensure a minimum of 3 months follow up period,
we required patients to have at least 3 months continuous eligibility period after the
“first-index date”. Anti-rheumatoid medications included traditional DMARDs, and
biologic DMARDS, defined by any drugs with AHFS codes or HIC3 codes as given
in Appendix C.
Analysis was conducted at panel level and not at individual level. This meant
that one person could contribute to the sample pool more than once. Each time a
person filled a prescription it triggers an insurance claim. We started with the first
known prescription claim for a DMARD (identified above as “first-index date”) and
followed all costs which occurred for the following 3 months including the day of
the prescription fill. We called this quarter as an episode of care. Any new
prescriptions or other claims which occurred during that episode get attributed to the
61
treatment started on that episode’s index date. Subsequently a prescription claim
anytime after the 90 days following the “first index date” triggers a new episode of
care and is followed for 3 more months. The first date of each following episode was
called the “episode index date”. Thus, each person can appear in the dataset multiple
number of times based on the number of eligible quarters he/she is observed in the
claims files. For an episode to be valid, the individual should also have continuous
enrollment in the eligibility files for the entire length of that quarter, beginning on
the index date of that particular episode. The selected patients were followed up till
the first occurrence of the following events: 1) disenrollment of Medicaid (defined
by an eligibility gap greater or equal to one month), 2) Death, or 3) December 2005.
Figure 3.1: Illustration of Study Design and Definitions
One-year pre-index 7-year Study Period
∇ ∇ ∇ ∇ ∇ ∇
JAN- 98 JAN-99 JAN-01 JAN-03 JAN05 DEC-05
∇: Prescription Fill for DMARD
: First Index Date
: Episode Index date
: First Episode (Duration-3 Months)
: Subsequent Episodes (Duration-3 Months)
: Initial Washout -period prior to “First” Index Date (Duration-12 Months)
: Pre-episode period prior to each “Episode” Index Date (Duration-6 Months)
In the example above, a patient has 6 prescription fills over the 8-year period,
and 5 of them are in the 7-year study period. However, only three episodes can be
found for this patient.
62
Exclusion Criteria-
1. Patients who visited a mental health institution in the pre-study period (defined as
the period 12 months prior to “first-line index” date) were excluded since, we cannot
ascertain components of the mental health care cost from the data uniquely. The
quality of life literature in RA has shown that high levels of disability lead to mental
distress, depression, and fatigue (Smedstad et al. 1996). Treatment of mental health
and apportioning the exact cost as RA related is difficult. Similarly, it is also difficult
to observe arthritis treatment decisions (drug therapies) of mental health patients.
They may follow very different behavior related to medication compliance compared
with the general population. To avoid these complications, we excluded patients who
visited a mental health institution in the 12 months prior to the “first- index date”.
2. Patients were excluded if they had one or more medical claims with a listed
diagnosis of Crohn's disease (555.xx), psoriasis (696.1), psoriatic arthritis (696.0), or
ankylosing spondylitis (720.0) during their pre-study history. These exclusionary
criteria were implemented to avoid including in the study sample patients who might
have received the agents of interest for another disease (because dosing may be
different for these indications compared with RA) (Weycker et al. 2005).
3. We excluded patients with established serious medical conditions identified during
the year before the cohort’s inception. These serious conditions include solid organ
transplantation, HIV/AIDS, and any indication of cancer (Grijalva et al. 2007).
63
Figure 3.2: Cohort Diagram of Inclusion/Exclusion Criteria
Total Patients
Remaining
= 6862
Original Medi-Cal Sample: 100% of the
Medi-Cal paid claims and eligibility
files for Medi-Cal enrollees from
01/01/1999 to 12/31/2005
Patient selection-
Diagnosis for RA & Rx
for any DMARDs &
Medi-Cal eligible
Exclusion Criteria 1-
Visit to a mental
health institution in
the pre-study period
Total Patients
Remaining
= 6677
Exclusion Criteria
2- Crohn’s disease
or psoriasis or
psoriatic arthritis, or
ankylosing
spondylitis
Total Patients Remaining = 6126
Final Sample Size after cleaning
Pharmacy Claims and deleting
those with zero days supply =
5921
Exclusion Criteria 3 -
Serious medical conditions -
organ transplantation,
HIV/AIDS, cancer, and age
not between 18 to 100 years
64
Final Sample-
A total of 5921 patients were found eligible for the creation of episodes,
based on all the exclusion criteria. Less than 5% of patients had combination therapy
and hence, they were deleted since, adequate cell sizes would not be available after
segregation into the biologic and non-biologic groups. Based on index treatment of
either of adalimumab, anakinra, etanercept, infliximab, hydroxychloroquine,
leflunomide, methotrexate, and sulfasalazine, episodes of care were created as
defined earlier. The only exclusion criteria applied to episodes was that if the patient
did not have continuous eligibility till the end date of the 90 days in that episode.
This exclusion was necessary to ascertain that we had all the valid claims for every
episode. Around 2.46% or 600 episodes were dropped due to inadequate eligibility
evidence. Thus, a total of 23,741 episodes were available for analysis.
On a practical issue, only N = 64 (0.27%) episodes were available for
infliximab treatment, similarly anakinra had N = 175 (0.74%) episodes, while
methotrexate had only N = 205 (0.86%) episodes. Estimation of treatment effects on
such low number of episodes was deemed futile especially considering these
episodes may actually represent just a handful of individual patients thus providing
no/low variation. Moreover, many of these patients may be dropped from the
analysis if missing data was encountered. Hence, the final analysis was conducted on
the drugs adalimumab, and etanercept representing the biologic DMARDs category
while hydroxychloroquine, leflunomide, and sulfasalazine comprised the standard
DMARDs category. Given these practical considerations, the analytical dataset
65
contained 5239 individual patients with a mean of 5 and maximum of 23 episodes
per patient, resulting in 23,297 total episodes.
3.3 EXPENDITURE AND COVARIATES
3.3.1. Quarterly expenditure
Starting from the index date, quarterly expenditure was measured repeatedly
for each eligible episode till the end of follow up. The total expenditure of therapy
was calculated on per-quarter per-member basis.
Two cost variables were constructed in the final episode level file, they were
episode total health care cost and pre-episode total health care cost which consisted
of total expenditure 6 months prior to the start of the episode. Episode total health
care cost was the outcome variable of interest in this study and included all the costs
incurred during that episode. Both cost variables were constructed in similar ways
and included the following components.
1) Hospital inpatient service cost:
Since, inpatient services are reimbursed by hospital inpatient days by Medi-
Cal, the average hospital inpatient day cost for Medi-Cal fee-for-service (FFS)
patient (excluding Medicare/Medi-Cal crossover claims) was assumed to be $1,000
and this amount was multiplied by the number of days spent in a hospital to calculate
hospital inpatient service cost.
2) Long term care cost: cost of services from skilled nursing facility (SNF) and
intermediate care facility (ICF).
66
Since, long term care (SNF and ICF) are reimbursed by days of service by
Medi-Cal, the average daily costs of SNF and ICF service for Medi-Cal fee-for-
service (FFS) was assumed to be $140 and this amount was multiplied by the length
of stay to obtain long tern care cost.
3) Other health care cost (e.g. pharmacy cost, physician outpatient cost etc.)
a. For non-Medicare/Medi-Cal crossover claims
Claim line costs were given in the data set.
b. For Medicare/Medi-Cal crossover claims
The total costs of the service assumed paid by Medicare were restored through
the Medicare deductible.
All the cost estimates were adjusted to 2007 dollars using the medical
component of the consumer price index (CPI). Study used contractual amounts
reimbursed by Medi-Cal to calculate treatment “cost” as opposed to “charges” or
“billed” amount since, cost represent actual transactions or transfers.
3.3.2. Covariates
Covariates included were patient-specific and provider specific variables
usually measured on or before the index date. These included
1) Socio-demographic variables:
This category included age, gender, race, population density in county of
beneficiary, dummy variables for county located in north of California (demarcated
by above or below Fresno county) and whether county was exclusive fee-for-service
county or not. Age was calculated as of each episode’s index date.
67
2) Comorbidities:
Major preexisting comorbidities were captured by Elixhauser comorbidity
index (Elixhauser et al. 1998). Another widely used option is the Charlson
comorbidity index (Charlson et al. 1987 and Deyo et al. 1992). The Elixhauser index
is a relatively newer comorbidity index for use with administrative data and is
generally considered superior to Charlson comorbidity index (Bing et al. 2008).
Hence, for this study comorbidity adjustment was undertaken by Elixhauser index.
The comorbidity index was calculated based on diagnosis codes of claims during the
6 months duration prior to the index date.
3) Exclusion Restrictions for Identification:
As mentioned in the section 2.2.3 above, without a set of variables which
appear in the selection equation but do not appear in the outcome equation, the
identification of treatment effects will depend on unobservable and untestable
distributional assumptions of joint normality. Specifically, an “exclusion restriction”,
defined as simultaneous omission of a variable(s) from the outcome equation and its
inclusion in the selection equation, is necessary for identification in cases where
explicit distributional assumptions are not invoked (Heckman and Robb 1985;
Cameron and Trivedi 2005). Furthermore, in the presence of heterogeneous
treatment effects and multiple endogenous treatments in the outcome equation, we
need a “unique” instrument to identify each drug individually (Heckman et al. 2006).
This requirement is extremely demanding since, the Medi-Cal insurance claims data
does not have many such options. Indeed a unique instrument strongly correlated to
68
one particular treatment, uncorrelated to the outcome model’s error and having no
direct impact on the outcome variable is next to impossible to find. Herein however,
lies the flexibility afforded by the nonlinear control function/generalized residual.
Since, it is a non-linear combination of the exogenous variables; identification can be
achieved by the non-linear functional form even if we do not have any exclusion
criteria. This approach is rarely justifiable and seldom used empirically.
For the current analysis, we do employ drug specific exclusion criteria.
Specifically, for each drug we create dummy variables which indicate
contraindication to that drug as published in the labeling information provided by the
manufacturer after FDA approval. The presence of a contraindication to a particular
treatment in the 6 months prior to the episode index date can be seen as exclusion
criteria, especially since, we specifically control for the pre-episode comorbidities.
We also specifically control for pre-episode total healthcare costs which should
further guarantee that the partial effects of these contraindications have no direct
effect on the outcome of interest. This approach has been used as exclusion criteria
in previous literature (Crown et al. 1988). Secondly, contraindications are clinically
important indicators while making treatment choice. Hence, we argue that these are
valid exclusion criteria although they may not be the ‘ideal’ exclusion variables. In
general, the correlation between the excluded variable(s) and the endogenous
treatment may be weak. However, given the claims data at hand, improving on this
problem is very difficult if not impossible.
69
The dummy indicators for presence of contraindications to a particular
treatment were constructed from the ICD-9 diagnosis in the 6 months prior to
episode index date. The lack of unrelated/exclusive contraindications amongst
leflunomide, hydroxychloroquine, and sulfasalazine was the main reason these three
drugs were all pooled into one category henceforth referred to as standard DMARD
(SDMRD). According to the manufacturer’s label, the contraindication for
adalimumab is presence of tuberculosis (TB) and hence, we created a dummy
variable for presence TB in 6 months prior to the episode index date. Similarly, the
dummy variable created as exclusion for etanercept was presence of sepsis in 6
month pre-episode period. For the combined category of SDMRD, dummies for
exclusion criteria were created as given below
1. Hydroxychroquine- ICD-9 for Pregnancy
2. Leflunomide- ICD-9 for Pregnancy, and abnormalities/diseases of Liver
3. Sulfasalazine- ICD-9 for Porphoryia and abnormalities/diseases of Liver and
Kidney
3.3.3. Treatment Indicators
Based on drug specific NDC procedure codes, the patients were categorized
according to those who use biologic DMARDs which include etanercept and
adalimumab and those using SDMRD which included leflunomide,
hydroxychloroquine, and sulfasalazine. The baseline comparator was SDMRD and
quarterly incremental differences from baseline were evaluated for adalimumab and
etanercept.
70
3.4 METHODOLOGY
The study design was a retrospective observational design using secondary
insurance claims data on California Medicaid enrollees. Econometric modeling was
employed to estimate the homogeneous and heterogeneous average treatment effect.
We modeled the treatment selection decision by comparing multinomial logit, nested
logit, and mixed logit error components model for treatment choice. In case of the
nested logit model, if and only if the inclusive value parameters lie in the range of 0
to 1 only then is the model consistent with random utility maximization theory
(RUT) (Maddala 1983; Greene 2002). The parameter of the inclusive value was
tested for consistency with RUT. The appropriate or true model for the selection
equation can be decided based on either of Hausman’s specification test, Wald,
Likelihood ratio (LR), and Lagrange multiplier (LM) tests. The Hausman test is
based on comparing a full choice model and a restricted model with few choices
eliminated. If the IIA assumption holds, then there should not be a large difference
between the parameters of the full choice model and the restricted choice model. If
the difference is significantly different from zero, then the multinomial choice model
is not the appropriate specification. Secondly, since, the multinomial logit model is a
special case of the more general, nested and mixed logit model when the inclusive
value parameter equals one, classical test procedures such as the Wald, LR, and LM
tests can be used (Hausman and McFadden 1984). We would have liked to compare
between the LM, LR, and Wald test to determine the proper model specification,
since, Hausman and McFadden have indicated that the asymptotically equivalent
71
classical tests differ markedly in their operating characteristics with the Wald being
the most powerful even in large samples (Hausman and McFadden 1984). However,
the SAS
®
, statistical software only provides the log-likelihood value for these
models. This only allows the calculation of the LR test, which is based on the
likelihood ratio, –2(Lr – Lu), where Lr is the log-likelihood value of the restricted
model, and Lu is the log likelihood value of the unrestricted model. It is important to
understand the exact model specification, since, based on this test we will form the
selection bias correction term and using that, construct the generalized residual.
Accepting the “true” model was based on LR statistic distributed as Chi
2
distribution
with degrees of freedom equaling the number of restrictions. The generalized
residual function was constructed as defined in the conceptual model, based on this
true model and using this as a benchmark the ATE and ATE1 from the other models
was compared to the treatment effects obtained from the true model.
The functional form of the observed explanatory variables for the treatment
choice model and outcome model are the same as described in the covariates section
above and the right hand side specification only differed in terms of the exclusion
criteria as explained. Identification of parameters in the outcome equation was thus,
not just based only on the non-linearity of the selection-bias correction term. To
avoid multicollinearity problem introduced by the selection-bias correction term, we
first need to assess the presence of multicollinearity. The standard approach is to use
Belsley, Kuh, and Welch’s conditional index (Belsley et al. 1980), however, its
implementation in panel data is cumbersome, especially since, we had interaction
72
terms. A second method to test for this multicollinearity is to regress the generalized
residual term on all of the other exogenous variables in the expenditure equation.
The explained variance (R
2
) from this regression indicates the strength of linear
association between the selection-bias correction term and the other variables. We
employed this method to assess multicollinearity.
Correlated random coefficients in endogeneity corrected fixed effects panel
data model were employed for estimating the treatment effects. As explained in the
conceptual model in Chapter 2, the endogeneity correction was achieved by adding
the appropriate generalized residual function term to the outcome expenditure
equation (Equation 20) using the procedure described in section 2.3. Heterogeneity
in treatment effects was allowed through the random coefficient’s interaction with
the generalized residual. Thus, the fixed effects panel data endogeneity corrected
model allows for heterogeneity in treatment response by allowing individual specific
intercepts and slopes to interact with the endogenous treatments and thus, with the
unobserved heterogeneity.
The model without the interaction terms assumes treatment homogeneity and
will thus provides an estimate of ATE1 using adapted formulas from Wooldridge
(2002). We estimated ATE and ATE1 of biologic DMARDs in this study while
controlling for unobservable factors contributing to the endogeneity in the outcomes
equation. The standard errors for the treatment effect parameters were obtained by
clustered bootstrapping techniques, where clustering was on patient level to allow for
panel nature of the data.
73
Chapter 4
Results
This chapter will describe the distribution of demographic variables,
comorbidities and exclusion restrictions and give the breakdown of episode
expenditures. We will then determine the appropriate selection model based on the
likelihood ratio test. After determining the influence of multicollinearity caused due
to inclusion of the generalized residual function, we will then determine if time
varying endogeneity is a source of bias and if it needs to be controlled. The last two
sections evaluate the influence of heterogeneity in treatment effects and controlling
for these individual idiosyncrasies, evaluate the average treatment effect.
For convenience, we reiterate the three fold objective of this dissertation. The
first objective was to assess and control for the endogeneity in treatment assignment
in this observational study. The second objective was to evaluate the impact of
employing different choice models used to describe treatment selection on the
estimated treatment effects. The last objective was to assess and control for the
correlation of unobserved heterogeneity with treatment indicators and thus control
for sorting on idiosyncrasies determining participation into treatment.
As mentioned in chapter 3, due to low sample sizes, methotrexate, anakinra,
infliximab, and combination therapy were not included in the final estimation.
Secondly, due to lack of unique identifying restrictions, the standard DMARDs had
to be pooled into a single group which also acted as baseline in evaluation of ATE
and ATE1. The final estimation sample had 23,297 observations on 5239
74
independent patients. The average number of episodes per individual was 5 with a
maximum of 23 episodes per individual.
4.1 DESCRIPTIVE STATISTICS
4.1.1 Distribution of Demographic Variables
The study sample had a mean (std. dev) age of 57.6 (14.4) years. As expected in
rheumatoid arthritis, majority of the sample was female (84.0%) belonging to
Caucasian race (38.2%). Demographic variables including age, gender, race,
population density, geographic location, and fee for service reimbursement in
patient’s county were unbalanced between the three treatment groups.
Table 4.1: Distribution of Demographic Covariates
Variable Mean (SD) or
Percentage of
Total
(N=5239)
Mean (SD)
or
Percentage
of
SDMRD
#
Mean (SD) or
Percentage
of
Adalimumab
Mean (SD)
or
Percentage
of
Etanercept
P -
Value
A
Age in years*
57.60 (±14.39) 58.01
(±14.34)
57.39 (±13.89) 55.80
(±14.64)
<0.001
Female 84.04% 84.69% 85.41% 80.65% <0.001
Caucasian 38.21% 37.73% 37.12% 40.71% <0.001
African American 10.72% 11.49% 10.04% 7.42% <0.001
Hispanic 16.33% 15.03% 28.47% 18.80% <0.001
Asian 13.78% 14.46% 8.65% 12.16% <0.001
Race- Others 20.26% 20.58% 14.93% 20.33% <0.001
County Population
Density x 10
3
(person/square
mile)*
4626.31
(± 4444.78)
4434.95
(± 4432.03)
6932.15
(± 4362.60)
4835.16
(± 4330.16)
<0.001
County with
Exclusive Fee for
Service
16.53% 17.47% 12.14% 13.49% <0.001
County in North of
California
30.50% 33.40% 15.55% 21.61% <0.001
A
: Probability from appropriate statistics: F-Distribution for joint significance of continuous
variables and Pearson
2
χ for discrete variables.
*
: Standard deviation in parenthesis for continuous variables
#: SDMRD = Standard DMARDs which was the pooled category including Leflunomide,
Sulfasalazine and Hydroxychloroquine
75
4.1.2 Distribution of Comorbidities and Exclusion Restrictions
The pre-episode Elixhauser comorbidities listed in Table 4.2 are excluding
RA comorbidity from the calculation. There was a statistically significant difference
between the treatments in pre-episode comorbidities (p < 0.001) as well as pre-
episode healthcare utilization (p < 0.001). Amongst the exclusion restrictions for
identification of the selection model, statistical differences were observed in
contraindications for drug use due to kidney diseases (p = 0.03), tuberculosis
(p = 0.04) and sepsis (p = 0.04).
Table 4.2: Distribution of Comorbidities and Exclusion Restrictions
Variable Mean (SD)
or
Percentage
of Total
(N=5239)
Mean (SD)
or
Percentage
of
SDMRD
#
Mean (SD) or
Percentage
of
Adalimumab
Mean (SD)
or
Percentage
of
Etanercept
P -
Value
A
Pre-Episode
Elixhauser*
1.15 (±1.34) 1.20 (±1.37) 1.0 (± 1.27) 0.97 (±1.21) <0.001
Pre-Episode Total
Expenditure*
$6827.16
(±10085.43)
$6083.20
(± 10133.01)
$9992.69
(±10372.52)
$9304.54
(±9174.30)
<0.001
Exclusion Criteria Variables
Pregnancy 0.32% 0.33% 0.36% 0.24% 0.61
Porphyria 0.11% 0.13% 0.09% 0.03% 0.21
Liver Diseases 2.91% 3.01% 2.01% 2.70% 0.11
Kidney- Diseases 1.93% 2.05% 1.82% 1.39% 0.03
Tuberculosis 0.33% 0.38% 0.18% 0.13% 0.04
Sepsis 0.04% 0.02% 0% 0.10% 0.04
A
: Probability from appropriate statistics: F-Distribution for joint significance of continuous
variables and Pearson
2
χ for discrete variables.
*
: Standard deviation in parenthesis for continuous variables
#: SDMRD = Standard DMARDs which was the pooled category including Leflunomide
Sulfasalazine and Hydroxychloroquine
4.1.3 Distribution of Episode Expenditures
Table 4.3 describes the total expenditure and also a breakdown of the various
sub-groups of expenditure. Total expenditure was a sum total of all the sub-groups of
expenditure listed in the table 4.3 for each episode. Statistically significant
76
differences were observed in total expenditure (p < 0.001), pharmacy expenditure
(p < 0.001), outpatient expenditure (p < 0.001), emergency department (p = 0.005)
and long-term care expenditure (p = 0.03). Pharmacy expenditure of biologic
DMARDs was significantly higher, while the SDMRD group had higher out-patient
expenditure and moderately high long term care expenditure as compared to the
biologics.
Table 4.3: Distribution of Quarterly/Episode Total Expenditures
Variable Mean (SD)
of Total
(N=5239) in
$
Mean (SD)
of
SDMRD
#
in
$
Mean (SD) of
Adalimumab
in
$
Mean (SD)
of
Etanercept
in $
P -
Value
A
Total Expenditure 4479.53
(± 7048.65)
3733.20
(± 6725.55)
7749.27
(± 6409.54)
6939.24
(± 7796.49)
<0.001
Pharmacy
Expenditure
2713.37
(± 2484.85)
1880.43
(± 1764.80)
6302.89
(± 2923.98)
5475.65
(± 2222.75)
<0.001
Outpatient
Expenditure
641.06
(± 1414.68)
680.17
(± 1500.57)
547.84
(± 1090.83)
489.76
(± 1030.68)
<0.001
Inpatient
Expenditure
566.98
(± 3990.23)
569.42
(± 3603.09)
447.85
(± 2055.32)
590.06
(± 5715.66)
0.56
Inpatient Physician
Expenditure
13.42
(± 139.77)
13.96
(± 140.29)
10.79
(± 145.98)
11.72
(± 135.52)
0.53
Emergency
Department
Expenditure
27.49
(± 158.82)
29.65
(± 169.90)
18.03
(± 86.60)
20.38
(± 116.82)
0.005
Long Term Care
(LTC) Expenditure
511.15
(± 4581.69)
552.61
(± 4683.37)
417.38
(± 4853.53)
349.27
(± 3992.43)
0.03
A
: Probability statistics: F-Distribution for joint significance of continuous variables.
#: SDMRD = Standard DMARDs which was the pooled category including Leflunomide
Sulfasalazine and Hydroxychloroquine
4.2 LIKELIHOOD RATIO TEST FOR SELECTION MODEL
We compared the log likelihood values computed from the three different
specifications of the selection model. The likelihood ratio test is distributed as
2
χ with degrees of freedom (DF) equal to number of restrictions imposed.
2
χ = 2*(LogL
u
- LogL
r
)
77
where, LogL
u
represents the log of unrestricted likelihood and LogL
r
is the log of
restricted likelihood at the optimized solution. When comparing the Multinomial
logit; the Nested and Mixed logit are the unrestricted models, while the Mixed logit
is the unrestricted model as compared to the Nested logit model. Mixed logit can
approximate any random utility model including the multinomial probit with the
right error specification and hence, it can nest all the other models (Hensher and
Greene 2001; Train 2003). Based on the LR test, we conclude that mixed logit is a
more appropriate choice model since, the other two models are rejected on the basis
of their restrictive assumptions.
Table 4.4: Treatment Selection Choice Model
Model Log
Likelihood
AIC Schwarz
Criterion
LR Test
Chi
2
P -Value
Multinomial vs. Nested Logit
–
p < 0.001 (DF = 2)
Multinomial Logit -12762.7 25705.38 26426.14
Multinomial vs. Mixed Logit
–
p < 0.001 (DF = 44)
Nested Logit -14071.0 28234.0 28602.0 Nested vs. Mixed Logit
–
p < 0.001 (DF = 42)
Mixed Logit -24405.0 48989.0 49710.0 -
4.3 MULTICOLLINEARITY DUE TO THE GENERALIZED RESIDUAL
Even when we use a non-linear form of the same explanatory variables
(excluding the identification restrictions based on contraindications) as the bias
correction term, it may still lead to multicollinearity in the second stage outcome
equation. We regressed the generalized residual term which was constructed using
the non-linear selection bias term (based on Lee’s (1983) correction) on the
exogenous variables in the outcome equation (Z
1it
from equation (20)). Table 4.5
78
shows that collinearity was not an issue without the addition of treatment indicators
to the model, however, when treatment indicators were added to the model,
collinearity was very strong. The second set of results was expected since, the
generalized residual is constructed using interactions of the treatment indicators with
the selection bias terms. The high R
2
in the second column is tautological by
definition of the generalized residual function. It does impact our analysis for the
mixed logit model, as will be evident in the results of ATE and ATE1 for that model.
Table 4.5: Correlation between Generalized Residual & Exogenous Variables
Model R
2
Excluding Treatment
Indicators
R
2
with Treatment Indicators
Multinomial Logit 0.00 0.99
Nested Logit 0.004 0.99
Mixed Logit 0.07 *
* Collinearity extremely strong, regressor dropped, hence, computed R
2
is incorrect
4.4 PRESENCE OF TIME VARYING ENDOGENEITY
To check for presence of time varying endogeneity in treatment assignment
we can use the t-distribution based statistical significance of the generalized residual
function. This is one of the advantages of control function based approaches which
provides straightforward test for treatment endogeneity. There was very strong
presence of time varying endogeneity as can be seen form the statistical significance
of the multinomial logit residual (p = 0.018) as well as the marginal significance of
the nested logit residual (p = 0.055). It is important to note that this endogeneity is
time varying since, the fixed effects model would have eliminated any time invariant
causes of endogeneity. Results from the mixed logit model are not available since,
the residual was dropped from the regression due to collinearity.
79
Table 4.6: Estimate and Significance of Generalized Residual
(Sample size N = 23297, Groups = 5239)
Clustered Bootstrap 1000 Reps Method Residual
Standard Error 95% CI
5% Lower
Bound
95% CI
95% Upper
Bound
Multinomial
Logit Correction
3200.68* 1355.96 543.04 5858.31
Nested Logit
Correction
4348.37 2264.15 -89.29 8786.03
Mixed Logit
Correction
#
a
: adjusted for all X and Z
1
variables in the models
*: significant at 95% CI
#: Residual dropped because of collinearity, hence, results cannot be generated
4.5 ESTIMATION OF ATE1 OR HOMOGENEOUS ATE
We estimated equation (20) from the conceptual model section, without the
interaction terms, hence, assuming homogeneity of treatment effect. Under this
assumption the average treatment effect in the treated is equal to the ATE1.
Although, the ATE1’s for adalimumab and etanercept were estimated in the same
regression model we have separated the results in two different tables for clarity
since, we are comparing treatment effects by 5 different models. Tables 4.9 and 4.10
in the following results for ATE were split for the same reason.
Although, time varying endogeneity was statistically significant (see table
4.6), for completeness, we have presented results from random effects and fixed
effects models which ignore this endogeneity. Based on Hausman’s test, the random
effects model was strongly rejected (
2
χ = 210.6, DF = 37, p < 0.001) in favor of the
fixed effects model. We then added the generalized residual function to the fixed
effects model to control for the time varying endogeneity.
80
As can be seen, accounting for this endogeneity resulted in significant increase in the
ATE1 estimate for adalimumab compared to standard DMARDs which is the
baseline for comparison. Secondly, there is a large difference in the parameter
estimates and the standard errors from the nested logit corrected outcome model as
compared to the multinomial logit corrected outcome model.
Table 4.7: Estimates of ATE1 Standard DMARD vs. Adalimumab
(Sample size N = 23297, Groups = 5239)
Clustered Bootstrap 1000 Reps Method Adalimumab
($)
Standard Error 95% CI
5% Lower
Bound
95% CI
95% Upper
Bound
Raw Mean
Difference
4016.07*
%
210.42 3603.62 4428.51
Random Effects
a
2397.61*
%
200.13 2005.35 2789.86
Fixed Effects
a
(FE)
2771.53*
%
285.44 2212.04 3331.02
FE-Multinomial
Logit Correction
a
10044.74* 3045.54 4075.59 16013.90
FE-Nested Logit
Correction
a
11808.78* 4638.20 2718.07 20899.49
FE-Mixed Logit
Correction
a
#
a: adjusted for all X and Z1 variables in the models
*: significant at 95% CI
#: Generalized Residual dropped because of collinearity, hence, results cannot be generated
%: Non-Bootstrapped parameters and standard errors
As can be seen from Table 4.8, accounting for time varying endogeneity
resulted in an increase in the ATE1 estimate for etanercept. Once again the nested
logit corrected model had higher parameter estimate as well as standard error as
compared to the multinomial model. As before, due to multicollinearity, the mixed
logit model parameters could not be estimated and this impact of collinearity was
true for the mixed logit corrected models for ATE as well.
81
Table 4.8: Estimates of ATE1 Standard DMARD vs. Etanercept
(Sample size N = 23297, Groups = 5239)
Clustered Bootstrap 1000 Reps Method Etanercept
($)
Standard Error 95% CI
5% Lower
Bound
95% CI
95% Upper
Bound
Raw Mean
Difference
3206.04*
%
120.75 2969.35 3442.72
Random Effects
a
1995.97*
%
126.57 1747.91 2244.04
Fixed Effects
a
(FE)
1881.38*
%
198.93 1491.46 2271.31
FE-Multinomial
Logit Correction
a
7841.72* 2539.46 2864.47 12818.96
FE-Nested Logit
Correction
a
11053.32* 4773.37 1697.69 20408.95
FE-Mixed Logit
Correction
a
#
a: adjusted for all X and Z1 variables in the models
*: significant at 95% CI
#: Residual dropped because of collinearity, hence, results cannot be generated
%: Non-Bootstrapped parameters and standard errors
Figure 4.1 and figure 4.2 below show the impact on ATE and ATE1, of
ignoring endogeneity, and also the impact of modeling the selection equation using
multinomial and nested logit specifications.
82
Figure 4.1: Graph Homogeneous Average Treatment Effect
Figure 4.2: Graph Heterogeneous Average Treatment Effect
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
Incremental Quarterly
Expenditure
Adalimumab Etanercept
ATE -Baseline Standard DMARDs
Raw Mean Difference Random Effects
Fixed Effects (FE) FE-Multinomial Logit Correction
FE-Nested Logit Correction
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
Incremental Quarterly
Expenditure
Adalimumab Etanercept
ATE1 -Baseline Standard DMARD
Raw Mean Difference Random Effects
Fixed Effects (FE) FE-Multinomial Logit Correction
FE-Nested Logit Correction
83
4.6 ESTIMATION OF HETEROGENEOUS ATE
To estimate the heterogeneous ATE, we estimated equation (20) as the
complete correlated random coefficients model described from the conceptual model
section. We included the interaction of the generalized residual with the de-meaned
exogenous variables, and the endogenous variables as well. This allows for the
treatment effect to be correlated to the unobserved heterogeneity. The random effects
and fixed effects are the same from ATE1 section and do not contain any
endogeneity correction terms or interactions. The results are restated only for
comparison.
Table 4.9: Estimates of ATE Standard DMARD vs. Adalimumab
(Sample size N = 23297, Groups = 5239)
Clustered Bootstrap 1000 Reps Method Adalimumab
($)
Standard Error 95% CI
5% Lower
Bound
95% CI
95% Upper
Bound
Raw Mean
Difference
4016.07*
%
210.42 3603.62 4428.51
Random Effects
a
2397.61*
%
200.13 2005.35 2789.86
Fixed Effects
a
(FE)
2771.53*
%
285.44 2212.04 3331.02
FE-Multinomial
Logit Correction
b
9321.84* 2474.22 4472.48 14171.22
FE-Nested Logit
Correction
b
13595.62* 4815.43 4157.56 23033.68
FE-Mixed Logit
Correction
b
#
a: adjusted for all X and Z1 variables in the models
b: adjusted for all X, Z1 and interaction variables in the models
*: significant at 95% CI
#: Residual dropped because of collinearity, hence, results cannot be generated
%: Non-Bootstrapped parameters and standard errors
The ATE of adalimumab as compared to standard DMARD shows a strong
increase in magnitude under the multinomial logit corrected model. This result is
even more amplified under the nested logit corrected outcome model where the
84
increase in magnitude is nearly 5 folds as compared to the naïve fixed effects model.
Similar results were also observed for etanercept where the ATE of etanercept on
total quarterly expenditure as compared to standard DMARD showed a strong
increase in magnitude under the multinomial logit as well as the nested logit
corrected model. The naïve fixed effects model ignoring time varying endogeneity
and heterogeneity in treatment effects, was nearly 7 times lower as compared to the
nested logit corrected heterogeneous ATE for etanercept. Unfortunately, the results
from mixed logit corrected model were lost due to multicollinearity. It would have
been interesting to compare the results from that model since, based on LR test, the
mixed logit had even rejected the nested logit model as being restrictive.
Table 4.10: Estimates of ATE Standard DMARD vs. Etanercept
(Sample size N = 23297, Groups = 5239)
Clustered Bootstrap 1000 Reps Method Etanercept
($)
Standard Error 95% CI
5% Lower
Bound
95% CI
95% Upper
Bound
Raw Mean
Difference
3206.04*
%
120.75 2969.35 3442.72
Random Effects
a
1995.97*
%
126.57 1747.91 2244.04
Fixed Effects
a
(FE)
1881.38*
%
198.93 1491.46 2271.31
FE-Multinomial
Logit Correction
b
9557.35* 3455.90 2783.91 16330.79
FE-Nested Logit
Correction
b
13973.11* 4823.84 4518.57 23427.66
FE-Mixed Logit
Correction
b
#
a: adjusted for all X and Z1 variables in the models
b: adjusted for all X, Z1 and interaction variables in the models
*: significant at 95% CI
#: Residual dropped because of collinearity, hence, results cannot be generated
%: Non-Bootstrapped parameters and standard errors
Thus, based on the likelihood ratio test for the selection model choice,
Hausman’s test to select between random and fixed effects models, and the t-test for
85
significance of the generalized residual to check time varying endogeneity, we
conclude that the true model is the fixed effects nested logit corrected model. This
inference is subject to the limitation that the estimates from the mixed logit corrected
model were lost to multicollinearity. The estimates for all the other models should be
deemed as biased.
Figure 4.3 and figure 4.4 on the following page underscore the importance of
controlling for heterogeneity in treatment effects. We can see a strong influence of
these assumptions on magnitude of the estimates.
86
Figure 4.3: Graph Comparing ATE to ATE1 in Adalimumab
Figure 4.4: Graph Comparing ATE to ATE1 in Etanercept
$9,322
$10,045
$13,596
$11,809
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
Incremental Quarterly
Expenditure
FE-Multinomial Logit Correction FE-Nested Logit Correction
ATE vs ATE1 in Adalimumab
Adalimumab ATE Adalimumab ATE1
$9,557
$7,842
$13,973
$11,053
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
Incremental Quarterly
Expenditure
FE-Multinomial Logit Correction FE-Nested Logit Correction
ATE vs ATE1 in Etanercept
Etanercept ATE Etanercept ATE1
87
Chapter 5
Discussion
The structural parameters of interest in this study were the heterogeneous
average treatment effect (ATE) and the homogeneous average treatment effect
(ATE1). Average treatment effect was defined as the impact of treatment on
quarterly total expenditure if RA patients were randomly assigned to biologic
DMARDs. We estimated these treatment effects while controlling the endogeneity in
treatment choice and allowing for heterogeneity in treatment effects.
The specific objectives of the study were :- (1) To assess and control for the
endogeneity in treatment assignment in this non-experimental study design. (2) To
assess the impact on estimated treatment effects when restrictive assumptions on
choice models were relaxed allowing more flexibility. (3) To evaluate the impact of
the correlation of unobserved heterogeneity with treatment choice and its impact on
the treatment effect parameters.
By employing an endogeneity corrected correlated random coefficients
model, we allow for a very general and realistic model to evaluate the comparative
effectiveness of multiple RA treatments on expenditure outcomes using an
observational study design.
We used a 100% sample of RA patients from the California Medi-Cal
eligible population. We used accepted and established methods for retrospective
study design using secondary data, to assemble a relatively homogeneous cohort of
88
RA patients with similar starting points of DMARD utilization. The unit of analysis
was an episode which was defined as a non-overlapping quarter (90 days) following
initiation of any of the study drugs. The unit of analysis was decided based on
clinical and statistical efficiency. Clinically, a quarter would be an appropriate unit
of time when effectiveness of treatment can be evaluated. Statistically, following
patients for a quarter as compared to yearly, allows for more variations, which is
useful when studying causal relationships or even when the research interest lies just
in estimating associations.
Covariates were defined based on previous literature and clinical knowledge
to limit the confounding effects which can bias parameters of interest. Univariate
analysis found these observable covariates to be statistically different between the
treatment groups. However, since, we were using insurance claims data to make
causal inferences; we had to make sure that we had accounted for all the observable
as well as unobservable confounders which could affect the final results.
Specifically, treatment selection amongst the biologic DMARDs should be based on
logistics, patient willingness or aversion to various medication delivery systems,
contraindications, co-morbidities, concomitant medications, susceptibility to
infection, and other factors which are unique for each patient (ACR Position
Statement 2006). Most of these variables were unobservable confounders in our
analysis or we had poor proxies (error in variables) for these variables. If we could
employ a randomized controlled trial (RCT) for assessment of the comparative
effectiveness, these unobserved confounders would not cause any problems in
89
estimation of treatment effects. The process of randomization ensures orthogonality
between the parameter of interest and the model’s error thus ruling out any
correlation that can induce bias. However, randomization is not an option since, we
are using secondary data. Secondly, even if it were an option, designing a trial for
head-to-head comparison of multiple treatments, especially when dealing with
economic outcomes which are notorious for small effect sizes and thus require large
sample size to power the study, would make undertaking such a study infeasible in
terms of cost. Lastly, although RCTs ensures high internal validity, the results
generally have narrow generalizability or external validity making them of limited
use to make policy decisions. Some of the other issues such as higher compliance,
Hawthorne effects and steady monitoring of the patients during the short trial periods
are the reasons for the differences in efficacy and effectiveness.
Retrospective databases such as the Medi-Cal can provide large sample sizes
on real world data over several years and thus have much better generalizability. The
huge problem in designing and analyzing these studies is to ensure internal validity.
One of the ways to increase internal validity is to make sure that we can minimize
the impact of the above mentioned unobservable confounders on the causal
parameters while adequately controlling for the effects of observable confounders.
Non-random assignment to treatment leads to endogenous regressors when we
cannot control for the unobservable confounders. Unless we control for endogeneity
we cannot estimate the causal effects since, the correlation between the explanatory
variables and the error term makes the parameter estimates biased. Specifically, the
90
regression coefficients incorrectly get credit for the variance explained by these
correlated omitted variables. Secondly, general estimation techniques rely on the
assumption of homogeneous treatment effects. The problem with medical outcomes
is that each patient responds to treatment differently. If treatment selection is made
based on this individual specific gain, then it needs to be controlled before estimating
causal effects. This phenomenon is termed as sorting on gains, and can be
appreciated in the current analysis where certain patients are assigned to a particular
treatment because that treatment will work better (unknown to the analyst) in that
particular patient. This induces another correlation of the treatment indicator with the
model’s error.
We used multiple regression based econometric techniques to handle
selection on unobservables and the heterogeneity in treatment effects. These methods
are generalizations of switching models widely used in econometrics. A latent index
for treatment selection was employed and assuming joint normality between the
errors of the latent model and the outcome model, we created an endogeneity
correction term. The estimates from standard IV do not estimate ATE in presence of
treatment heterogeneity since, the conditional homoskedasticity of covariance
assumption does not hold when treatment is discrete. These are all of the issues that
need to be addressed for internal validity of the current study.
We used Lee’s (1983) approach to create a selection bias correction term
since, we had a polychotomous choice model which has type-I extreme value error
distribution. Assuming joint normality distribution when one of the marginal
91
distributions is not normal will not hold. Lee’s transformation converts the extreme
value error to its standard normal form while maintaining all the properties of the
primary variable. However, Lee’s approach was meant to handle sample selection
models which are essentially estimated on partial observations. We do not have any
censoring of the data and hence, the approach had to be modified to create a
generalized residual to address endogeneity. This is essentially a control function
approach when the endogenous variable is discrete with polychotomous choice set.
The control function approach comes with the additional assumption that the latent
index/selection model is correctly specified in terms of functional form of the
exogenous regressors as well as the specification of the model. Given this
assumption it is important to understand how the treatment effect varies as a function
of the latent index model specification. Based on the Likelihood ratio tests we
confirmed that the flexible mixed logit model was the true latent index model. In fact
the widely used multinomial logit was the least preferred model amongst the three
choice models studied. Future studies estimating heterogeneous treatment effects
should select the index model with care especially when dealing with multiple
treatments.
One of the problems of using a generalized residual or even the selection bias
correction term is whether the structural parameters are identifiable. We have used
six contraindications indicators in pre-episode six month interval to avoid having to
address identification based on joint normality assumption. We believe, after
partialing out the effects of pre-episode comorbidities and expenditures there is no
92
residual effect of these variables on the outcome, directly. However, the correlation
between these exclusion restrictions and the endogenous treatment variables may be
small. In that case, identification is still technically possible however, the results are
less robust. The second problem created by including the generalized residual is
multicollinearity. We found that collinearity was not an issue if the treatment
indicators were not included in the model assessing the linear correlation. This may
be due to the use of the six exclusion variables and the non-linearity of the selection
bias correction term. Upon addition of the treatment indicators however,
multicollinearity was very strong, especially in the mixed logit case where no
treatment effects could be estimated as the generalized residual dropped out of the
model due to collinearity. The high R
2
is tautological since, by construction the
treatment indicators are interacted with Lee’s selection bias correction term to form
the generalized residual.
Intuitively, the selection bias term constructed using Lee’s approach
represents the probability of not receiving the treatment given that the individual was
'at risk' of receiving the treatment. As the probability of receiving the treatment
approaches 1, selection bias term approaches 0. Thus, for patients who actually
receive the treatment, if the predicted probability of receiving the treatment is high
based upon observable factors, the influence of unobservable variables is small and
consequently the bias is small. This predicted probability is derived based on the
assumption that the treatment choice model is correctly specified. To clarify this
point, consider the case that the true treatment assignment is by the nested or mixed
93
logit specification and instead we specify a multinomial logit model as treatment
choice equation. In this case, if the selection bias term approaches zero, it may
erroneously give the impression that we are accounting for most observable variables
that are actually responsible for receiving the treatment, while the influence of
unobservable variables is insignificant. Thus, we may conclude that the risk of
selection bias is low, even when the true treatment decision was made according to
the nested/mixed logit model. However, the predicted probabilities from the
nested/mixed logit are different from the multinomial logit, and we can only account
for selection bias, if we specify an appropriate treatment choice model. Furthermore,
the treatment selection equation should capture the factors hypothesized to influence
treatment selection (Crown et al. 1988).
Another problem when using the latent index based approach is the
heteroskedasticity introduced due to the use of estimated values or generated
regressors instead of true values of the selection bias term in the outcomes equation.
The heteroskedasticity may be present in the structural error and hence, sandwich
correction will not address that issue (Imben and Wooldridge 2007). Lastly, we also
used sample means instead of population expected value to de-mean the exogenous
covariates in the correlated random coefficients model. This further creates improper
standard errors. To overcome all these issues we estimated consistent standard errors
by 1000 replications using clustered bootstrapping. The clustering was at the
individual patient level to address the panel nature of the data.
94
The control functions approach offers a simple “t” test based on the
bootstrapped errors to reject the null hypothesis of exogeneity. The bootstrapped
t-value for the generalized residual based on the multinomial logit as well as the
nested logit confirmed the presence of time-varying endogeneity. These results are
important since, they point that using a naïve fixed effects panel data approach or
differences-in-differences approach would not have solved for the endogeneity. Most
models using retrospective panel data methods avail to the property of fixed effects
to eliminate endogeneity and other confounding bias. In the current case, since,
endogeneity was time varying, it cannot be controlled using just the fixed effects
model and warrants the addition of the generalized residual. These results also
indicate that a random effects model is grossly misspecified as it simply assumes
away the problem through strict exogeneity of the regressors.
The addition of the generalized residual to the fixed effects model had strong
impact on the magnitude of ATE1 estimate of adalimumab and etanercept. As
compared to naïve fixed effects model, the ATE1 estimate of adalimumab more than
tripled in magnitude and remained statistically significant with the multinomial logit
corrected residual. This indicates a negative selection bias since, accounting for
unobserved effects increased the magnitude of the treatment parameter. Similar
results were observed for etanercept as well where the parameter estimate
quadrupled in magnitude in the multinomial logit corrected model as compared to
the naïve fixed effects model. Although endogeneity increased the magnitude of the
parameter, however, in a multiple regression framework we cannot in general apriori
95
predict the impact that selection bias can have on the parameter estimate (Maddala
1983). The above results also held true in case of the nested logit corrected model.
Heterogeneous average treatment effect (ATE) of adalimumab under the restrictive
multinomial logit corrected model was significantly higher as compared to the naïve
fixed effects model; however, now the magnitude decreased as compared to the
multinomial logit based homogeneous average treatment effect (ATE1).
Furthermore, ATE of adalimumab as compared to standard DMARD under the
nested logit corrected outcome model had a much higher magnitude as compared to
the multinomial logit corrected ATE. The ATE for etanercept was statistically
significant under either of the endogeneity corrected models however, unlike the
case for adalimumab, an increase in magnitude was observed under both endogeneity
corrected models. The ATE parameter estimate from the nested logit corrected
model however, was much higher as compared to the multinomial logit corrected
estimate. Moreover, the standard errors from the nested logit corrected models were
larger than the multinomial logit in both the biologic treatment’s ATEs.
These results are interesting since, they point out very important sources of
bias when estimating comparative effectiveness. Firstly, the results point out the
need to control for time varying endogeneity in panel data models and not assume
that endogeneity and heterogeneity is time invariant. Ignoring endogeneity and
heterogeneity will give rise to grossly incorrect estimates of treatment effects which
are biased even asymptotically. Secondly, when applying marginal treatment effects
approach in estimating heterogeneous treatment effects especially when treatment is
96
discrete choice, the specification of latent index model matters. It is very important
to understand the exact choice model to estimate unbiased parameters. Lastly, the
large difference in ATE1 and ATE should be convincing not to assume
homogeneous treatment effects. Sorting on gains or (unknown to the analyst)
patients receiving treatments that are more likely to work for them and its impact on
treatment choice is an important source of bias in medical outcomes. Moreover, this
bias is such that we cannot decide apriori about its existence and conservative
approach is to allow for such difference through model specification (Heckman et al.
2006). In this study, the heterogeneity bias affected only the magnitude of the
parameter. Given the right (strongly correlated) instruments, even the sign on the
coefficient as well as the statistical significance of the point estimate has the
potential to change.
All these issues have tremendous impact on policy. Under one set of
assumptions, we may accept a policy to be cost-effective and under another set of
assumptions we may reject adoption of the same policy. Models need to be realistic
to mimic real life decisions to be helpful in making important policy decisions. We
have shown that the panel data correlated random coefficients model with
endogeneity correction is a practical and realistic tool to assess treatment effects in
any disease. Moreover, the model and its assumptions can be adapted and replicated
in most secondary data since, we did not have access to nor have we created any
specialized instruments for estimation. In the current environment where
comparative effectiveness studies are demanded for making policy decisions, the
97
methodology presented in this dissertation offers solutions for comparing multiple
treatments simultaneously with results that have high generalizability and adequate
internal validity using retrospective observational study design.
Study Limitations
The usual limitations of retrospective analysis apply to the current study as
well. In addition, although the selection bias correction term controls for unobserved
factors in the treatment decision, it does not account for all unobservable factors.
Omission of relevant regressor in the expenditure equation will still lead to a
misspecified model and omitted variable bias will apply. The only solution is to
rigorously perform extensive specification testing for autocorrelation in the residuals,
correlations between the residuals and the explanatory variables, heteroskedasticity,
or other deviations from a normal distribution.
A stronger limitation is the joint normality assumption between the errors of
the outcome and selection equation. Many authors have argued for and against this
assumption. The current trend in treatment effects literature relies more on the
competing potential outcomes framework for treatment effects as opposed to the
traditional structural framework. However, as mentioned in Chapter 2, under the
potential outcomes framework the identification of ATE and ATE1 rely on the
existence of a valid instrument when selection is on unobservable factors correlated
to treatment and outcome. Moreover, if treatment effects are heterogeneous and we
have multiple treatments to compare, standard IV assumption are ineffective and we
need to generalize the current tools to allow for accurate estimation. Unfortunately,
98
in multiple treatments with heterogeneous treatment effects, the joint normality
assumption is indispensable. If we have valid exclusion criteria we do not have to
rely on this assumption for identification and moreover if the selection model is
correctly specified then ATE is identifiable using the correlated random coefficients
model formulated as described in chapter 2 above.
Our study only followed patients for a maximum of 28 quarters and this
limited follow-up may bias the results against the biologic DMARDs. The biologic
DMARDs have the potential to decrease disease progressions and may show
considerable saving in terms of avoided total hip replacements and other such
expensive surgical procedure expected in the 10 year time horizon of RA patients.
We also had problems with the results from the mixed logit model. Although
this model is very flexible, it’s also very demanding in terms of data. Since, we did
not have any choice specific variables in the model and relied only on individual
specific variables, this model could not differentiate between choices correctly. This
was evident from the single predicted probability produced for each treatment choice
by this model. Furthermore, the variations in individual level exogenous variables
had no impact on the predicted probability. In other words, the non-missing
predicted probability was exactly the same for all observations and treatments (in
fact it was 0.33 for each treatment). Given this single number as predicted
probability for the entire sample, its no surprise that there was near perfect
multicollinearity in this model. To avoid this issue, we varied between the following
frameworks for the mixed logit- 1) normal error components, 2) uniform error
99
components, 3) normal distributed random coefficients 4) log-normal distributed
random coefficients, 5) uniform distributed random coefficients 6) Bounds on the
coefficients using above mentioned 5 models. However, none of the strategies made
a difference on the estimated probabilities. Except for a small change in magnitude;
the predictions were exactly identical for the entire sample irrespective of other
exogenous variables or treatments. Furthermore, the covariance matrix was a zero
matrix. One reason may be the large number of regressor used in the model since,
generally; mixed logit models are estimated with very few choice specific variables.
However, since, the mixed logit is a non-linear model we cannot drop any regressor
since, even an orthogonal (to included regressor) omitted variable with produce
biased parameter vector and thus biased probabilities. We conclude that specifying a
mixed logit without regressors varying over choices as opposed to individuals and
the inclusion of large number of explanatory variables maybe an overambitious goal
in retrospective database study. These complex models need much more informative
data such as that obtain from choice experiments.
Conclusion
We estimated the average treatment effect of adding biologic DMARD to the
treatment of RA patients and found that the incremental quarterly expenditure under
adalimumab and etanercept can be significantly higher if patients currently on
standard DMARD treatment are randomly assigned to these expensive biologic
DMARDs. We found evidence of strong impact of index model specification on the
magnitude and standard errors on the parameters of treatment effects. The above
100
mentioned results are based on the nested logit model specification for the latent
index. We also found evidence of heterogeneity in treatment effects and controlled
for the heterogeneity through a panel data correlated random coefficients model.
101
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Appendix A
Specification of the Nesting Structure
RA Patient
Treatment
Choice
Biologic
DMARDs
Standard
DMARDs
Adalimumab Etanercept Leflunomide Hydroxy-
chloroquine
Sulfasalazine
118
Appendix B
1
st
Line Agents used in RA Treatment
(A) Hydroxychloroquine (HCQ), (B) Sulfasalazine (SSZ), (C) Methotrexate (MTX),
(D) Leflunomide, (E) Etanercept, (F) Infliximab + MTX,
(G) Azathioprine (AZA), (H) D-Penicillamine (D-Pen),
(I) Gold, Oral, (J) Gold, Intramuscular,
(K) Staphylococcal Protein A, (L) Minocycline, (M) Cyclosporine
2
nd
line agents used in RA treatment
Standard Combination DMARDs for RA-
A) Leflunomide + Other DMRDs,
B) Methotrexate + Hydroxychloroquine + Sulfasalazine
C) Methotrexate + Sulfasalazine + Prednisone Taper
D) Methotrexate + Sulfasalazine
E) Methotrexate + Leflunomide
F) Methotrexate + Cyclosporine
G) Hydroxychloroquine + Cyclosporine
The most commonly used combinations are MTX-HCQ, MTX-SSZ, and SSZ-HCQ.
Biologic DMARDS for RA-
a) Etanercept
b) Infliximab
c) Adalimumab
d) Anakinra
119
Appendix C
AHFS and HIC3 Codes-
AHFS CODES AHFS Description
81220 Sulfonamides (Systemic)
100000 Anti-neoplastic Agents
280804 Non-steroidal Anti-Inflammatory Agents
600000 Gold Compounds
8122000 Sulfonamides (Systemic)
10000000 Anti-neoplastic Agents
28080408 Cyclooxygenase-2 (Cox-2) Inhibitors
52089200 Anti-Inflammatory Agents, Misc.
60000000 Gold Compounds
HIC3 HIC3 Description
S2B NSAIDs, Cyclooxygenase Inhibitor - Type
S2C Gold Salts
S2I Anti-Inflammatory, Pyrimidine Synthesis Inhibitor
S2J Anti-Inflammatory Tumor Necrosis Factor Inhibitor
S2M Anti-Flam. Interleukin-1 Receptor Antagonist
S2N Anti-Arthritic, Folate Antagonist Agents
Z2E Immunosuppressive
120
Appendix D
ICD-9 Codes for Inclusion Criteria
ICD-9 Codes:
714
714.0
714.1
714.2
714.4
714.8
714.81
714.89
121
Appendix E
Complete Regression Tables
Naive Fixed Effects
Variable Coefficient Bootstrap
Error
z P>|z| Lower 5%
[95% Conf.
Interval]
Upper 95%
[95% Conf.
Interval]
Adalimumab 2771.53 285.44 9.71 0.00 2212.04 3331.02
Etanercept 1881.38 198.93 9.46 0.00 1491.46 2271.31
Pre Episode
Total
Expenditure
0.20 0.01 30.55 0.00 0.18 0.21
Pre Episode
Elixhauser
-168.39 43.00 -3.92 0.00 -252.66 -84.11
North County 1358.18 593.01 2.29 0.02 195.82 2520.54
FFS County -364.84 580.63 -0.63 0.53 -1502.94 773.26
Population
Density in
County
0.09 0.05 1.67 0.10 -0.01 0.19
White 2314.90 420.41 5.51 0.00 1490.86 3138.94
Black 1701.91 1033.68 1.65 0.10 -324.22 3728.03
Hispanic 76.03 280.92 0.27 0.79 -474.60 626.66
Asian 383.63 249.93 1.53 0.13 -106.27 873.52
Episode Age -66.22 122.07 -0.54 0.59 -305.48 173.04
Quater1 2347.39 1600.24 1.47 0.14 -789.25 5484.02
Quater2 2170.08 1560.84 1.39 0.16 -889.33 5229.49
Quater3 2174.60 1538.66 1.41 0.16 -841.34 5190.54
Quater4 2500.17 1527.51 1.64 0.10 -493.92 5494.25
Quater5 2994.09 1514.38 1.98 0.05 25.76 5962.43
Quater6 3004.70 1497.66 2.01 0.05 69.14 5940.26
Quater7 3112.07 1482.00 2.10 0.04 207.20 6016.95
Quater8 3159.21 1469.57 2.15 0.03 278.70 6039.73
Quater9 3248.03 1459.47 2.23 0.03 387.32 6108.74
Quater10 3170.04 1447.27 2.19 0.03 333.24 6006.83
Quater11 3406.69 1434.94 2.37 0.02 594.06 6219.33
Quater12 3216.59 1424.34 2.26 0.02 424.74 6008.43
Quater13 3485.35 1414.73 2.46 0.01 712.33 6258.38
Quater14 3438.26 1406.11 2.45 0.01 682.14 6194.37
Quater15 3587.78 1397.68 2.57 0.01 848.18 6327.37
Quater16 3391.10 1390.24 2.44 0.02 666.10 6116.10
Quater17 3540.84 1380.86 2.56 0.01 834.22 6247.47
Quater18 3725.13 1373.37 2.71 0.01 1033.18 6417.08
Quater19 4018.63 1367.41 2.94 0.00 1338.38 6698.89
Quater20 3839.52 1362.89 2.82 0.01 1168.12 6510.92
Quater21 4010.35 1357.23 2.95 0.00 1350.04 6670.66
Quater22 4317.66 1353.25 3.19 0.00 1665.15 6970.17
Quater23 4491.50 1349.49 3.33 0.00 1846.37 7136.64
Quater24 4621.98 1346.81 3.43 0.00 1982.09 7261.87
Quater25 4508.71 1344.61 3.35 0.00 1873.13 7144.29
Quater26 4711.27 1341.86 3.51 0.00 2081.10 7341.45
Quater27 4484.20 1345.13 3.33 0.00 1847.59 7120.80
Constant 1029.86 7444.86 0.14 0.89 -13562.84 15622.56
122
Multinomial Logit Corrected Model for Homogeneous Treatment Effect
Variable Coefficient Bootstrap
Error
z P>|z| Lower 5%
[95% Conf.
Interval]
Upper 95%
[95% Conf.
Interval]
Adalimumab 10044.74 3045.54 3.30 0.00 4075.59 16013.90
Etanercept 7841.72 2539.46 3.09 0.00 2864.47 12818.96
Multinomial
Residual
3200.68 1355.96 2.36 0.02 543.04 5858.31
Pre Episode
Total
Expenditure
0.16 0.03 5.84 0.00 0.11 0.21
Pre Episode
Elixhauser
16.29 83.12 0.20 0.85 -146.61 179.20
North County 1934.08 798.97 2.42 0.02 368.13 3500.02
FFS County -199.55 645.34 -0.31 0.76 -1464.40 1065.29
Population
Density in
County
0.08 0.08 0.95 0.34 -0.08 0.24
White 2319.06 1436.66 1.61 0.11 -496.74 5134.86
Black 2183.00 846.83 2.58 0.01 523.25 3842.74
Hispanic 95.32 214.73 0.44 0.66 -325.54 516.17
Asian 522.87 220.81 2.37 0.02 90.09 955.66
Episode Age -46.34 112.70 -0.41 0.68 -267.23 174.55
Quater1 2892.65 3476.82 0.83 0.41 -3921.79 9707.08
Quater2 2254.87 3500.04 0.64 0.52 -4605.08 9114.82
Quater3 2266.89 3469.12 0.65 0.51 -4532.47 9066.25
Quater4 2707.74 3486.78 0.78 0.44 -4126.22 9541.70
Quater5 3120.95 3460.05 0.90 0.37 -3660.62 9902.52
Quater6 3193.68 3452.11 0.93 0.36 -3572.33 9959.69
Quater7 3256.98 3457.22 0.94 0.35 -3519.05 10033.00
Quater8 3270.70 3436.11 0.95 0.34 -3463.96 10005.35
Quater9 3528.53 3422.60 1.03 0.30 -3179.64 10236.71
Quater10 3446.33 3412.75 1.01 0.31 -3242.54 10135.20
Quater11 3652.49 3414.08 1.07 0.29 -3038.98 10343.95
Quater12 3404.75 3405.68 1.00 0.32 -3270.26 10079.76
Quater13 3623.71 3398.62 1.07 0.29 -3037.47 10284.89
Quater14 3732.92 3391.79 1.10 0.27 -2914.86 10380.70
Quater15 3914.30 3399.38 1.15 0.25 -2748.36 10576.96
Quater16 3739.79 3372.45 1.11 0.27 -2870.10 10349.67
Quater17 3571.79 3371.28 1.06 0.29 -3035.80 10179.39
Quater18 3535.18 3379.76 1.05 0.30 -3089.02 10159.39
Quater19 3775.28 3373.47 1.12 0.26 -2836.59 10387.16
Quater20 3502.48 3371.41 1.04 0.30 -3105.36 10110.32
Quater21 3627.52 3371.84 1.08 0.28 -2981.17 10236.21
Quater22 3836.12 3394.68 1.13 0.26 -2817.32 10489.56
Quater23 3978.40 3372.22 1.18 0.24 -2631.04 10587.83
Quater24 4091.73 3392.52 1.21 0.23 -2557.49 10740.95
Quater25 3986.65 3376.37 1.18 0.24 -2630.91 10604.21
Quater26 4024.97 3372.24 1.19 0.23 -2584.50 10634.44
Quater27 3818.52 3368.49 1.13 0.26 -2783.59 10420.64
Constant -1371.34 8044.79 -0.17 0.87 -17138.84 14396.15
123
Multinomial Logit Corrected Model for Heterogeneous Treatment Effect
Variable Coefficient Bootstrap
Error
z P>|z| Lower
5%
[95%
Conf.
Interval]
Upper
95%
[95%
Conf.
Interval]
Adalimumab 9321.84 2474.22 3.77 0.00 4472.47 14171.22
Etanercept 9557.35 3455.90 2.77 0.01 2783.91 16330.79
Multinomial Residual 8074.08 2594.49 3.11 0.00 2988.98 13159.19
AdalimumabXResidual -6591.09 2234.53 -2.95 0.00 -10970.70 -2211.48
EtanerceptXResidual -5148.32 1823.22 -2.82 0.01 -8721.76 -1574.88
Pre Episode Total
Expenditure
0.11 0.03 4.20 0.00 0.06 0.17
Pre Episode Elixhauser 212.79 117.32 1.81 0.07 -17.15 442.73
North County 1478.12 824.68 1.79 0.07 -138.22 3094.46
FFS County 287.89 765.98 0.38 0.71 -1213.40 1789.17
Population Density in
County
0.13 0.13 0.98 0.33 -0.13 0.39
White 472.58 348.64 1.36 0.18 -210.74 1155.89
Black 2085.57 601.30 3.47 0.00 907.03 3264.10
Hispanic 4.53 220.70 0.02 0.98 -428.03 437.10
Asian 607.52 219.44 2.77 0.01 177.41 1037.62
Episode Age -41.62 120.43 -0.35 0.73 -277.66 194.42
Quater1 3552.64 3702.47 0.96 0.34 -3704.07 10809.34
Quater2 2301.05 3763.42 0.61 0.54 -5075.11 9677.21
Quater3 2477.17 3722.55 0.67 0.51 -4818.88 9773.23
Quater4 3038.33 3730.23 0.81 0.42 -4272.79 10349.45
Quater5 3354.55 3705.54 0.91 0.37 -3908.17 10617.28
Quater6 3496.61 3695.42 0.95 0.34 -3746.28 10739.50
Quater7 3506.94 3701.15 0.95 0.34 -3747.18 10761.05
Quater8 3494.45 3685.14 0.95 0.34 -3728.29 10717.18
Quater9 3942.31 3656.05 1.08 0.28 -3223.40 11108.03
Quater10 3841.11 3649.79 1.05 0.29 -3312.35 10994.57
Quater11 4023.27 3652.15 1.10 0.27 -3134.82 11181.35
Quater12 3729.47 3646.65 1.02 0.31 -3417.84 10876.77
Quater13 3893.04 3641.84 1.07 0.29 -3244.83 11030.91
Quater14 4182.80 3623.99 1.15 0.25 -2920.08 11285.68
Quater15 4400.65 3627.62 1.21 0.23 -2709.35 11510.66
Quater16 4250.07 3598.60 1.18 0.24 -2803.06 11303.20
Quater17 3621.64 3628.27 1.00 0.32 -3489.63 10732.91
Quater18 3282.41 3662.18 0.90 0.37 -3895.32 10460.15
Quater19 3483.62 3658.42 0.95 0.34 -3686.75 10653.98
Quater20 3146.31 3667.14 0.86 0.39 -4041.15 10333.77
Quater21 3230.68 3671.02 0.88 0.38 -3964.39 10425.75
Quater22 3382.51 3699.85 0.91 0.36 -3869.06 10634.08
Quater23 3466.97 3680.47 0.94 0.35 -3746.61 10680.55
Quater24 3529.90 3700.40 0.95 0.34 -3722.76 10782.56
Quater25 3500.39 3685.91 0.95 0.34 -3723.86 10724.65
Quater26 3399.49 3691.52 0.92 0.36 -3835.76 10634.74
Quater27 3147.99 3690.02 0.85 0.39 -4084.31 10380.29
Constant -2676.86 8586.78 -0.31 0.76 -19506.64 14152.93
124
Multinomial Logit Corrected Model for Heterogeneous Treatment Effect
(Continued) Interaction Terms
Variable Coefficient Bootstrap
Error
z P>|z| Lower
5%
[95%
Conf.
Interval]
Upper
95%
[95%
Conf.
Interval]
Pre_TotexpXAdalimumab 0.11 0.10 1.09 0.28 -0.09 0.30
Pre_TotexpXEtanercept -0.01 0.09 -0.15 0.88 -0.18 0.15
Pre_ElixXAdalimumab 259.41 306.86 0.85 0.40 -342.03 860.86
Pre_ElixXEtanercept -146.12 181.75 -0.80 0.42 -502.33 210.10
North
CountyXAdalimumab
14701.98 14450.89 1.02 0.31 -13621.24 43025.20
North CountyXEtanercept -243.42 1202.36 -0.20 0.84 -2600.01 2113.16
FFS
CountyXAdalimumab
-5663.11 11612.31 -0.49 0.63 -28422.82 17096.61
FFS CountyXEtanercept -181.24 1105.94 -0.16 0.87 -2348.84 1986.37
Population
CountyXAdalimumab
-0.45 0.36 -1.27 0.20 -1.15 0.25
Population
CountyXEtanercept
-0.02 0.22 -0.09 0.93 -0.46 0.42
Episode
AgeXAdalimumab
50.57 181.53 0.28 0.78 -305.22 406.36
Episode AgeXEtanercept 36.95 141.03 0.26 0.79 -239.46 313.37
WhiteXAdalimumab 541.15 1909.03 0.28 0.78 -3200.49 4282.78
WhiteXEtanercept 8270.75 6011.89 1.38 0.17 -3512.34 20053.84
BlackXEtanercept -202.94 14486.17 -0.01 0.99 -28595.30 28189.43
HispanicXAdalimumab 3011.25 2039.81 1.48 0.14 -986.70 7009.19
HispanicXEtanercept 86.92 732.60 0.12 0.91 -1348.95 1522.80
AsianXAdalimumab 3886.44 2781.38 1.40 0.16 -1564.97 9337.85
AsianXEtanercept -213.21 734.12 -0.29 0.77 -1652.05 1225.63
125
Nested Logit Corrected Model for Homogeneous Treatment Effect
Variable Coefficient Bootstrap
Error
z P>|z| Lower 5%
[95% Conf.
Interval]
Upper 95%
[95% Conf.
Interval]
Adalimumab 11808.78 4638.20 2.55 0.01 2718.07 20899.49
Etanercept 11053.32 4773.37 2.32 0.02 1697.69 20408.95
Nested Logit
Residual
4348.37 2264.15 1.92 0.06 -89.29 8786.03
Pre Episode
Total
Expenditure
0.15 0.03 4.96 0.00 0.09 0.21
Pre Episode
Elixhauser
73.87 115.06 0.64 0.52 -151.65 299.39
North County 2140.93 876.06 2.44 0.02 423.88 3857.99
FFS County -197.14 640.63 -0.31 0.76 -1452.75 1058.47
Population
Density in
County
0.07 0.08 0.80 0.42 -0.10 0.23
White 2304.97 1435.49 1.61 0.11 -508.53 5118.47
Black 2285.03 952.55 2.40 0.02 418.07 4151.99
Hispanic 80.36 218.13 0.37 0.71 -347.17 507.89
Asian 590.73 262.07 2.25 0.02 77.08 1104.39
Episode Age -61.05 112.66 -0.54 0.59 -281.85 159.76
Quater1 3106.53 3498.01 0.89 0.37 -3749.43 9962.50
Quater2 2431.46 3520.18 0.69 0.49 -4467.96 9330.88
Quater3 2450.85 3488.71 0.70 0.48 -4386.89 9288.60
Quater4 2879.34 3505.91 0.82 0.41 -3992.13 9750.81
Quater5 3304.04 3479.13 0.95 0.34 -3514.92 10123.00
Quater6 3410.18 3470.79 0.98 0.33 -3392.43 10212.80
Quater7 3455.66 3476.22 0.99 0.32 -3357.61 10268.93
Quater8 3458.10 3455.17 1.00 0.32 -3313.91 10230.11
Quater9 3762.23 3441.27 1.09 0.27 -2982.55 10507.00
Quater10 3681.78 3429.64 1.07 0.28 -3040.18 10403.75
Quater11 3891.84 3430.37 1.13 0.26 -2831.57 10615.24
Quater12 3638.12 3423.89 1.06 0.29 -3072.59 10348.82
Quater13 3871.85 3415.57 1.13 0.26 -2822.55 10566.24
Quater14 3987.13 3408.90 1.17 0.24 -2694.18 10668.45
Quater15 4180.23 3416.45 1.22 0.22 -2515.89 10876.34
Quater16 4021.19 3389.51 1.19 0.24 -2622.12 10664.51
Quater17 3712.16 3394.49 1.09 0.27 -2940.91 10365.23
Quater18 3559.44 3414.67 1.04 0.30 -3133.19 10252.07
Quater19 3784.40 3410.70 1.11 0.27 -2900.44 10469.24
Quater20 3484.67 3413.48 1.02 0.31 -3205.62 10174.96
Quater21 3558.41 3421.44 1.04 0.30 -3147.49 10264.32
Quater22 3750.41 3439.94 1.09 0.28 -2991.74 10492.57
Quater23 3875.51 3427.10 1.13 0.26 -2841.49 10592.50
Quater24 3994.45 3446.85 1.16 0.25 -2761.25 10750.14
Quater25 3886.96 3431.90 1.13 0.26 -2839.45 10613.37
Quater26 3862.00 3442.09 1.12 0.26 -2884.37 10608.36
Quater27 3667.41 3434.04 1.07 0.29 -3063.18 10398.00
Constant -1027.07 8076.61 -0.13 0.90 -16856.93 14802.79
126
Nested Logit Corrected Model for Heterogeneous Treatment Effect
Variable Coefficient Bootstrap
Error
z P>|z| Lower
5%
[95%
Conf.
Interval]
Upper
95%
[95%
Conf.
Interval]
Adalimumab 13595.62 4815.43 2.82 0.01 4157.56 23033.68
Etanercept 13973.11 4823.84 2.90 0.00 4518.56 23427.66
Nested Logit Residual 9948.31 3174.20 3.13 0.00 3727.01 16169.62
AdalimumabXResidaul -6182.62 2023.53 -3.06 0.00 -10148.67 -2216.57
EtanerceptXResidual -5314.89 1972.11 -2.70 0.01 -9180.16 -1449.62
Pre Episode Total
Expenditure
0.09 0.03 3.15 0.00 0.04 0.15
Pre Episode Elixhauser 310.55 143.60 2.16 0.03 29.10 592.01
North County 1689.53 848.13 1.99 0.05 27.22 3351.85
FFS County 353.11 768.05 0.46 0.65 -1152.24 1858.47
Population Density in
County
0.12 0.13 0.93 0.35 -0.14 0.38
White 450.76 347.35 1.30 0.19 -230.05 1131.56
Black 2272.78 641.64 3.54 0.00 1015.19 3530.37
Hispanic -2.61 220.19 -0.01 0.99 -434.17 428.95
Asian 691.08 234.20 2.95 0.00 232.05 1150.11
Episode Age -3.65 117.35 -0.03 0.98 -233.64 226.35
Quater1 4432.96 3717.87 1.19 0.23 -2853.93 11719.84
Quater2 3071.46 3773.15 0.81 0.42 -4323.77 10466.69
Quater3 3269.31 3734.28 0.88 0.38 -4049.74 10588.35
Quater4 3793.87 3747.13 1.01 0.31 -3550.36 11138.10
Quater5 4117.34 3718.99 1.11 0.27 -3171.76 11406.43
Quater6 4308.86 3709.96 1.16 0.25 -2962.53 11580.25
Quater7 4280.07 3716.45 1.15 0.25 -3004.04 11564.19
Quater8 4243.98 3701.52 1.15 0.25 -3010.86 11498.82
Quater9 4767.62 3673.01 1.30 0.19 -2431.35 11966.59
Quater10 4668.57 3665.53 1.27 0.20 -2515.75 11852.88
Quater11 4841.48 3667.68 1.32 0.19 -2347.04 12029.99
Quater12 4533.72 3663.99 1.24 0.22 -2647.57 11715.00
Quater13 4717.23 3657.61 1.29 0.20 -2451.55 11886.01
Quater14 5017.69 3641.52 1.38 0.17 -2119.57 12154.94
Quater15 5247.62 3645.72 1.44 0.15 -1897.86 12393.09
Quater16 5116.00 3616.28 1.41 0.16 -1971.77 12393.09
Quater17 4272.57 3651.51 1.17 0.24 -2884.26 11429.39
Quater18 3769.95 3694.77 1.02 0.31 -3471.67 11011.58
Quater19 3941.58 3694.49 1.07 0.29 -3299.47 11182.64
Quater20 3546.35 3707.45 0.96 0.34 -3720.11 10812.81
Quater21 3547.95 3721.00 0.95 0.34 -3745.07 10840.97
Quater22 3664.83 3750.95 0.98 0.33 -3686.89 11016.55
Quater23 3723.97 3738.44 1.00 0.32 -3603.23 11051.18
Quater24 3794.84 3757.96 1.01 0.31 -3570.63 11160.30
Quater25 3744.77 3744.72 1.00 0.32 -3594.74 11084.29
Quater26 3526.54 3768.15 0.94 0.35 -3858.91 10911.98
Quater27 3323.01 3759.68 0.88 0.38 -4045.83 10691.84
Constant -6129.83 8448.70 -0.73 0.47 -22688.97 10429.31
127
Nested Logit Corrected Model for Heterogeneous Treatment Effect
(Continued) Interaction Terms
Variable Coefficient Bootstrap
Error
z P>|z| Lower
5%
[95%
Conf.
Interval]
Upper
95%
[95%
Conf.
Interval]
Pre_TotexpXAdalimumab 0.11 0.10 1.05 0.29 -0.09 0.30
Pre_TotexpXEtanercept 0.00 0.08 -0.03 0.98 -0.16 0.16
Pre_ElixXAdalimumab 334.76 323.46 1.03 0.30 -299.21 968.74
Pre_ElixXEtanercept -140.66 162.12 -0.87 0.39 -458.40 177.08
North
CountyXAdalimumab
15004.04 14313.03 1.05 0.30 -13048.98 43057.07
North CountyXEtanercept -260.85 1181.45 -0.22 0.83 -2576.44 2054.74
FFS
CountyXAdalimumab
-5279.50 11494.89 -0.46 0.65 -27809.07 17250.08
FFS CountyXEtanercept -417.30 1086.73 -0.38 0.70 -2547.24 1712.64
Population
CountyXAdalimumab
-0.39 0.36 -1.11 0.27 -1.09 0.30
Population
CountyXEtanercept
-0.08 0.21 -0.36 0.72 -0.49 0.34
Episode
AgeXAdalimumab
9.05 173.77 0.05 0.96 -331.53 349.62
Episode AgeXEtanercept -117.73 130.92 -0.90 0.37 -374.34 138.88
WhiteXAdalimumab 529.07 1840.73 0.29 0.77 -3078.70 4136.84
WhiteXEtanercept 8265.13 5998.81 1.38 0.17 -3492.32 20022.57
BlackXEtanercept -269.56 14888.12 -0.02 0.99 -29449.73 28910.61
HispanicXAdalimumab 2860.01 2064.25 1.39 0.17 -1185.84 6905.86
HispanicXEtanercept 46.00 718.98 0.06 0.95 -1363.18 1455.18
AsianXAdalimumab 3659.10 2821.55 1.30 0.20 -1871.03 9189.23
AsianXEtanercept -29.02 785.28 -0.04 0.97 -1568.14 1510.11
Abstract (if available)
Abstract
We estimated the treatment effects of biologic disease modifying anti-rheumatoid drugs (DMARDs) on the quarterly total health-care expenditure, while controlling non-random assignment to treatment (endogeneity) and allowing heterogeneity in treatment effects. The structural parameters, heterogeneous (ATE), and homogeneous (ATE1) average treatment effects were defined as the impact of treatment on quarterly total health-care expenditure, if patients are randomly assigned to biologic DMARDs.
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Asset Metadata
Creator
Kawatkar, Aniket Arun
(author)
Core Title
Estimation of heterogeneous average treatment effect-panel data correlated random coefficients model with polychotomous endogenous treatments
School
School of Pharmacy
Degree
Doctor of Philosophy
Degree Program
Pharmaceutical Economics
Publication Date
05/11/2009
Defense Date
01/22/2009
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
average treatment effect,comparative effectiveness,correlated random coefficients model,OAI-PMH Harvest,panel data,treatment effect heterogeneity
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Nichol, Michael B. (
committee chair
), Hay, Joel W. (
committee member
), Stohl, William (
committee member
)
Creator Email
aniket_k22@hotmail.com,kawatkar@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m2233
Unique identifier
UC1206722
Identifier
etd-Kawatkar-2700 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-239497 (legacy record id),usctheses-m2233 (legacy record id)
Legacy Identifier
etd-Kawatkar-2700.pdf
Dmrecord
239497
Document Type
Dissertation
Rights
Kawatkar, Aniket Arun
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
average treatment effect
comparative effectiveness
correlated random coefficients model
panel data
treatment effect heterogeneity