Semiparametric efficient and robust estimation of treatment effect from observational data Öffentlichkeit
Li, Li (2011)
Abstract
Abstract
Semiparametric efficient and robust estimation of treatment effect
from observational data
By Li Li
This dissertation aims to solve two problems. One is to evaluate
the effect of treatment switching strategies in HIV studies and the
second is to evaluate the effect of treatment duration in infusion
studies.
The optimal timing of switching ARV therapy in HIV studies to
ensure sustained virologic suppression and prolonged clinical
stability in patients who
have rebound in their HIV RNA is not known. Randomized clinical
trials to compare early versus delayed switching have been
difficult to design. Here, we provide a statistical framework to
compare early versus late regimen change using observed data from
the ACTG A5095 study. We also propose a nonparametric method as an
alternative method when semiparametric method does not perform very
well at small sample size, having high dimensional confounding and
a highly skewed outcome. Simulation studies showed that
nonparametric methods had smaller MSE than semiparametric method
for the cases mentioned above.
The second topic is motivated by a treatment duration-response
study, ESPRIT (Enhanced Suppression of the Platelet IIb/IIa
receptor with Integrilin Therapy) trial. The experimental treatment
regimen consisted of a continuous infusion for 18-24 hours for
coronary artery disease with a similar regimen for the placebo
group. The study protocol also required that patients experiencing
serious complications immediately discontinue the infusion process.
Once treatment is found to be effective, attention often focuses on
optimum treatment delivery. A treatment duration policy for t
unites of time is defined as a recommendation to treat for t units
of time or until a treatment-terminating event occurs, whichever
comes first. Johnson and Tsiatis (2004) have shown how to
consistently estimate the population mean response for the
treatment policy. We propose a more efficient and doubly robust
estimator to protect again model misspecification using
semiparametric theory by defining potential outcomes and regarding
observed data
as the coarsened full data.
Table of Contents
Contents
1 Introduction 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 1
1.1.1 The ACTG A5095 Data . . . . . . . . . . . . . . . . . . . . .
1
1.1.2 ESPRIT infusion trial . . . . . . . . . . . . . . . . . . . .
. . 5
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 6
1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 8
2 Optimal Estimation of Mean Endpoint on Two-stage Sequential
Antiretroviral Treatment Regimen Using Observational HIV Data
11
2.1 Introduction and Background . . . . . . . . . . . . . . . . . .
. . . . 11
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 13
2.2.1 Causal Model: Notation and Assumptions . . . . . . . . . . .
13
2.2.1.1 Potential outcome framework . . . . . . . . . . . . .
13
2.2.1.2 Identiability and Consistency . . . . . . . . . . . .
13
2.2.1.3 Treatment assignment . . . . . . . . . . . . . . . . .
14
2.2.2 Estimation in the observational study . . . . . . . . . . . .
. . 15
2.2.2.1 Hypothetical two-stage trial . . . . . . . . . . . . . .
15
2.2.2.2 The Radon-Nikodym derivative . . . . . . . . . . . .
16
2.2.3 Doubly-Robust, Locally Ecient, and Optimal Estimation . .
18
2.2.3.1 Semiparametric AIPW class of estimators . . . . . .
19
2.2.3.2 The regression estimator . . . . . . . . . . . . . . . .
20
2.2.4 Estimating Equations and Asymptotic Variance . . . . . . . .
22
2.2.5 Length-adjusted Area Under the Curve . . . . . . . . . . . .
. 23
2.3 Analysis of the ACTG A5095 data . . . . . . . . . . . . . . . .
. . . 24
2.3.1 The study sample . . . . . . . . . . . . . . . . . . . . . .
. . . 24
2.3.2 Treatment and endpoint denitions . . . . . . . . . . . . . .
. 25
2.3.3 Main Analysis . . . . . . . . . . . . . . . . . . . . . . . .
. . . 28
2.3.4 Sensitivity analyses . . . . . . . . . . . . . . . . . . . .
. . . . 33
2.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 35
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 41
3 Locally efficient and Double Robust Semiparametric Estimator for
the Treatment Duration, with Duration Possibly Right-censored
44
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 44
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 45
3.2.1 Full Data and Observed Data . . . . . . . . . . . . . . . . .
. 46
3.2.2 Coarsening Variable and Link Functions . . . . . . . . . . .
. 49
3.2.3 Partially-monotone Coarsening . . . . . . . . . . . . . . . .
. 50
3.2.4 Inuence Functions of Full Data and Observed Data . . . . . .
54
3.2.5 Projection . . . . . . . . . . . . . . . . 67
3.2.6 MLE Approach to Estimate the Parameters in the Cause-specific
Hazard Function estimation . . . . . . . . . . . . . . . . . . . .
75
3.2.7 Adaptive Estimation to Estimate Conditional Means and
Distribution of Terminating Event . . . . . . . . . . . . . . . . .
77
3.2.8 Estimating the Asymptotic Variance . . . . . . . . . . . . .
. 78
3.3 Properties of Proposed Estimator . . . . . . . . . . . . . . .
. . . . . 79
3.3.1 Double Robustness of Proposed Estimator . . . . . . . . . . .
79
3.3.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 87
3.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 89
3.5 Analysis of the ESPRIT Infusion Trial . . . . . . . . . . . . .
. . . . 91
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 93
4 Nonparametric Method Using Boosting Algorithm To Estimate Mean
Potential Outcomes 95
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 96
4.1.1 Nonparametric Regression . . . . . . . . . . . . . . . . . .
. . 96
4.1.2 Boosting Algorithms . . . . . . . . . . . . . . . . . . . . .
. . 98
4.1.3 Decision Tree . . . . . . . . . . . . . . . . . . . . . . . .
. . . 104
4.1.4 Nonparametric Regression Analysis with Missing data . . . . .
109
4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 110
4.2.1 Point Estimate . . . . . . . . . . . . . . . . . . . . . . .
. . . 111
4.2.2 Variance Estimate . . . . . . . . . . . . . . . . . . . . . .
. . 113
4.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 114
4.4 Application to ACTG A5095 Data . . . . . . . . . . . . . . . .
. . . 118
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 119
5 Summary and Future Work 123
About this Dissertation
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