Statistical Methods for Causal Inference in Observational Studies Public

Abstract

Observational studies, such as those of patient registries may oth er valuable patient and disease information that is impossible to study in a randomized trial, but often pose unique challenges that require special care in estimating a causal eff ect of treatment. This dissertation is motivated by a registry of patients with amyotrophic lateral sclerosis (ALS) maintained by the Emory ALS Clinic, in which the non-random receipt of the treatment, that is, the insertion of a Percutaneous Endoscopic Gastrostomy (PEG) tube, is time-dependent and both the receipt of treatment and clinical outcomes are subject to "censoring" by death. In order to identify a causal eff ect of PEG treatment on an outcome, we incorporate and build upon various causal inference methods such as principal stratification and propensity score matching.

After a review of current literature and a more detailed description of the data in Chapter 1, we develop a fully Bayesian modeling approach to estimate the survivor average causal eff ect (SACE) of PEG on BMI, which is a surrogate outcome measure of nutrition and quality of life, using propensity score methods within a principal stratification framework in Chapter 2. Chapter 3 investigates propensity process matching for estimating treatment eff ect in observational studies. The Propensity Process is a method that is able to address complex features that are common to observational registries with longitudinally measured data. Matching by Propensity Process outperforms the naive analysis and other non-binary propensity score methods and achieves covariate balance across treatment groups. Chapter 4 extends the methods presented in Chapter 2 to address outcomes that are missing due to a lapse in clinic visits. A single framework incorporating principal stratification using post-treatment survival outcomes, as well as models for the mechanism of missing outcomes and generalized propensity score is used for an unbiased estimation of treatment eff ect.

Finally, potential future work is explored in Chapter 5. The data of the ALS registry is rich with complications that could inspire new directions of research, and there is significant interest in the issues of observational studies in the statistical community to fuel this methodological research.

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 1

1.1 Amyotrophic Lateral Sclerosis and the Motivating Dataset . . . . . . . . . . . . . 2
1.2 Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Rubin's Causal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 Propensity Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.3 Principal Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2.4 Data Augmentation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Estimating treatment effect in observational studies in the presence

of censoring due to death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.1 Framework for Causal Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.2 Generalized Propensity Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.3 Principal Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.4 Bayesian Framework for Estimation and Inference . . . . . . . . . . . . . . . . . 29
2.3 Application to Emory ALS Clinic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3.1 Balance of Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.2 Estimation of SACE of PEG Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43

3 Propensity function matching for estimating treatment effect . . . . . . . . . . . . 47

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.1.1 Data of the Emory ALS Clinic Registry. . . . . . . . . . . . . . . . . . . . . . . . . 49

3.1.2 Propensity Score Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2 Time-varying Propensity Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Propensity Process: Estimation and Matching . . . . . . . . . . . . . . . . . . . . . 56

3.3.1 Generalized Propensity Score Using Baseline Variables . . . . . . . . . . . . . 57

3.3.2 Time-Varying GPS and Propensity Process . . . . . . . . . . . . . . . . . . . . . . 58

3.3.3 Definitionof Risk Sets and Matching . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.3.4 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4 Analysisof Data from ALS Registry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4 Estimating the palliative effect of percutaneous endoscopic gastrostomy in an

observational registry in the presence of missing outcome data . . . . . . . . . . . 69

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2.1 Framework for Causal Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.2 Generalized Propensity Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.3 Principal Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2.4 Missing Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.2.5 Bayesian Framework for Estimation and Inference . . . . . . . . . . . . . . . . 80
4.3 Application to Emory ALS Clinic Data . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3.1 Estimation of SACE of PEG Treatment . . . . . . . . . . . . . . . . . . . . . . . . 85

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5 Future Directions for Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.1 Observed Data Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.2 Prior Distributions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.3 Imputation Probabilities for I-Step . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.4 Full Conditional Distributions of Parameters of Interest in the
P-step of the Data Augmentation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 96

A.4.1 Full Conditional Distributions of αg . . . . . . . . . . . . . . . . . . . . . . . . . . 96

A.4.2 Full Conditional Distributions of ηg . . . . . . . . . . . . . . . . . . . . . . . . . . 97

A.4.3 Full Conditional Distributions of σ²g . . . . . . . . . . . . . . . . . . . . . . . . . 97

A.5 Summary of Patient Characteristics at Several Timepoints . . . . . . . . . . . 98

B Appendix for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.1 Proof of Propositions 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

C Appendix for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

C.1 Observed Data Likelihood for Modelling Approach 2 . . . . . . . . . . . . . . . 104
C.2 Prior Distributions of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

C.3 Imputation Probabilities for I-Step. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

C.4 Full Conditional Distributions of Parameters of Interest in the

P-step of the Data Augmentation Algorithm . . . . . . . . . . . . . . . . . . . . . . . 107

C.4.1 Full Conditional Distributions of αg . . . . . . . . . . . . . . . . . . . . . . . . . 107

C.4.2 Full Conditional Distributions of θg,z . . . . . . . . . . . . . . . . . . . . . . . . 108

C.4.3 Full Conditional Distributions of ηg . . . . . . . . . . . . . . . . . . . . . . . . . 108

C.4.4 Full Conditional Distributions of σ²g . . . . . . . . . . . . . . . . . . . . . . . . 108

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics Statistics
Mot-clé	Propensity Score Methods Propensity Process Censoring by Death Principal Stratification Observational Studies Missing Data
Committee Chair / Thesis Advisor	Long, Qi, Emory University Johnson, Brent, University of Rochester Medical Center
Committee Members	Chang, Howard, Emory University Lyles, Robert, Emory University Glass, Jonathan D, Emory University

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