Semiparametric efficient and robust estimation of treatment effect from observational data Public

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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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics
Mot-clé	semiparametric statistical method
Committee Chair / Thesis Advisor	Johnson, Brent, Emory University
Committee Members	Long, Qi, Emory University Hanfelt, John, Emory University Sullivan, Patrick S, Emory University

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