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

Lu, Xin (2015)

Permanent URL: https://etd.library.emory.edu/concern/etds/4x51hj75m?locale=en
Published

Abstract

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

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 likelihood . . . . . . . . . . . . . . . . . . . . . . . . 16

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

List of Figures

1.1 Survival curves for patients who experience adverse events in 30 days 3

1.2 Survival curves for patients who experience virologic failure from ATCG

Study A5095 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Comparisons of estimates (solid circles) and their 95% con_dence intervals

(line lengths) form ESPRIT trial . . . . . . . . . . . . . . . . 34

2.2 Mean outcomes across switch time estimated by direct estimator based

on Weibull model (red), direct estimator based on Cox proportional

hazard model (green) and inverse probability weighting estimator from

Johnson and Tsiatis (2004) (blue) with their respective 95% con_dence

intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

A.1 Estimated CD4+ counts and their 95% con_dence intervals across

switch time using our direct estimator based on Cox PH models and

linear regression (red), Cox PH models and spline regression (green),

and Cox PH models and generalized additive models (blue). . . . . . 115

List of Tables

2.1 Simulation results for the discrete time setting . . . . . . . . . . . . . . . 28

2.2 Simulation results from the continuous time setting . . . . . . . . . . . . 31

3.1 Simulation results for estimation on the potential outcome for n=300 46

3.2 Simulation results for estimation on the linear trend of potential outcomes

across time for n=300 . . . . . . . . . . . . . . . . . . . . . . 46

4.1 Table of possible values for KbUc when estimating _m. . . . . . . . . . 54

4.2 Table of values for weights when estimating _1. . . . . . . . . . . . . 58

4.3 Table of values for weights when estimating _2. . . . . . . . . . . . . 59

4.4 Simulation results for estimating the average potential outcomes . . . 81

A.1 Simulation results for IPW estimator with varying binning strategy at

continuous time setting . . . . . . . . . . . . . . . . . . . . . . . . . . 110

A.2 Estimates of coe_cients (and their standard errors) for outcome logistic

regression on adverse event within 30 days and Cox proportional hazard

regression with respect to infusion time . . . . . . . . . . . . . . . . . 112

A.3 Estimated event proportion (and their standard errors) for the ESPRIT

trial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

A.4 Parameter estimates for outcome regression on CD4 cell count and Cox

proportional hazard regression with respect to time to switch . . . . . 113

A.5 ACTG data analysis with CD4 outcome . . . . . . . . . . . . . . . . 114

About this Dissertation

Rights statement
  • Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
School
Department
Degree
Submission
Language
  • English
Research field
Keyword
Committee Chair / Thesis Advisor
Committee Members
Last modified

Primary PDF

Supplemental Files