Estimation of Potential Outcomes when Treatment Assignment and Discontinuation Compete in Observational Data Open Access

Lu, Xin (2015)

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In clinical studies, randomization of treatment lengths may not be feasible in practice, resulting in the confounding of treatment effects. Moreover, treatment decisions may be missing due to treatment-terminating events. Therefore, to estimate the mean outcome across treatment lengths while accounting for the above obstacles, we propose several new estimators using causal inference theory and methods for different treatment assignment settings. In the first project, we propose a new direct estimator for the mean outcome of a target treatment length policy using outcome regression. The estimator works well in both discrete and continuous time. We exemplify the direct estimator through small sample numerical studies and the analysis of two real data sets and show the direct estimator is more precise. In many dynamic regimes, patients' treatment plan may vary with changes in their clinical characteristics that measured at routine clinic visits, which may also be confounded with patients' outcomes. To taking into account of the time-varying effects, in the second project, we implemented the G-computational algorithm in outcome regression with two approaches to estimate the mean potential outcome on treatment length policies. In simulation studies, our approaches are more efficient compared to an existing inverse probability weighting estimator. It could also approximate the distribution as well as the mean of the potential outcomes. To maintain the consistency of our estimators proposed in the previous two projects, the outcome regression models must be correctly specified, which may not be always met. To achieve a consistent estimation under moderate miss-specification, under the same dynamic regime setting as project 2, we propose a doubly-robust estimator and an improved doubly-robust estimators for estimating the mean potential outcomes while adjusting for time-varying effects. They demonstrate desirable properties for small samples in simulation studies and the improved doubly robust estimator achieves minimum variance even when the outcome regression model may be miss-specified.

Table of Contents

1 Introduction 1

1.1 Introduction 1

1.1.1 The Enhanced Suppression of the Platelet IIb/IIIa Receptor with Integrilin Therapy (ESPRIT) trial 1

1.1.2 AIDS Clinical Trials Group Study A5095 2

1.1.3 Causal Inference 4

1.2 Outline 10

2 Direct Estimation of the Mean Outcome amidst Early Treatment Stoppage 13

2.1 Introduction 13

2.2 Methods 16

2.2.1 Data and likelihood16

2.2.2 The estimand 19

2.2.3 Direct Estimation 21

2.3 Large Sample Properties 24

2.4 Simulation Studies 26

2.4.1 Treatment Assignment on a Finite Set 26

2.4.2 Treatment Assignment in Continuous Time 29

2.5 Data Applications 32

2.5.1 ESPRIT Infusion Trial Data 32

2.5.2 Switch to Second-line ART in ACTG A5095 33

2.6 Remark 35

3 Estimation of the Distribution of Potential Outcomes amidst Early Treatment Stoppage in the Presence of Time-Varying Confounders 37

3.1 Introduction 37

3.2 Methods 38

3.2.1 Observed Data 38

3.2.2 Proposed method 39

3.3 Simulation Studies 43

3.3.1 Data Simulation 43

3.3.2 Monte Carlo Integration by G-computational Algorithm 45

3.3.3 Direct Prediction by G-computational Algorithm 45

3.3.4 Simulation Results 47

3.4 Remarks 47

4 Doubly Robust Estimation of Potential Outcomes amidst Early Treatment Stoppage in the Presence of Time-Varying Confounders 49

4.1 Introduction 49

4.2 Methods 51

4.2.1 Observed Data 51

4.2.2 Doubly Robust Estimation Framework 52

4.2.3 Estimation with Two-Stage Designs 57

4.2.4 Improved doubly-robust estimators under the simpli_ed scenario 65

4.3 Simulation Studies 78

4.3.1 Data Simulation 78

4.3.2 Simulation Results 80

4.4 Remarks 83

5 Conclusions 85

Bibliography 85

A Supplementary Material for Chapter 2 93

A.1 Details of Large Sample Properties 93

A.2 Details of Binning Strategies for Inverse Probability Weighting Estimator110

A.3 Details of ESPRIT Infusion Trial Data Analysis Results 111

A.4 Details of ACTG Data Analysis Results 113

B Supplementary Material for Chapter 4 117

B.0.1 Derivation of doubly robust estimators 117

B.0.2 Connection of 4.2.3 to Chapter 1 125

C R codes 127

C.1 R codes for Chapter 3 127

C.2 R codes for Chapter 4 149

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