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Issues in Causal Inference and Applications to Public Health

Price, Megan Emily (2009)
Dissertation (166 pages)
Committee Chair / Thesis Adviser: Hertzberg, Vicki S
Committee Members: Frankel, Michael ; Long, Qi ; Lyles, Robert ; Waller, Lance
Research Fields: Health Sciences, Public Health
Keywords: Causal inference
Program: Laney Graduate School, Biostatistics
Permanent url: http://pid.emory.edu/ark:/25593/19dnh

Abstract

Abstract
Issues in Causal Inference and Applications to Public Health
By Megan Price
We present three examples of public health research problems for which causal inference
methods are better suited than commonly used traditional analytical methods. We
expand and generalize our causal inference approaches in systematic ways to provide
insight into their potential use beyond these specific motivating examples.
First is adjusting for confounding in observational studies. Although
there is a growing trend to use propensity score analyses to confirm results from traditional
adjustment methods, there has been little systematic comparison of propensity score and
traditional regression adjustment methods, particularly when the majority of confounders are dichotomous variables. This leaves open the question of how to interpret
potentially conflicting results from the two methods. We simulate comparison groups with
higher and lower frequencies of confounders, and compare the performance of traditional
and propensity score methods in terms of estimated treatment effect.
Next, we examine the performance of Frangakis and Rubin's (2002) principle stratification
method for estimating treatment effects when outcome measures are `truncated' by death.
In our example from the ProTECT study [Wright et al., 2007] of traumatic brain injury
patients, we have the added complication of missing mortality status due to loss to follow-
up. We are not aware of any other research that examines the performance of principle
stratification analyses when the post-randomization variable upon which stratification is
based is missing among some observations. We examine the sensitivity of causal effect esti-
mates to assumptions about the structure of the principle strata themselves versus possible
patterns of missingness, and show that, for our example, the former are more
influential.
Last, there have been recent efforts to define a prognostic score for stroke and traumatic
brain injury patients, to enable tailoring of definitions of `favorable' outcomes based on a
patient's predicted outcome. We propose a new application of Hansen's (2006,
2008) prognostic scoring methods to this problem, and compare our prognostic score results
to those generated by prognostic models from the existing literature. We
also conduct a formal power analysis comparing analyses using outcomes based on a patient's
prognosis versus traditional outcome measures.

Table of Contents

Contents
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Causal Inference - General . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Independence and the Stable-Unit-Treatment-Value Assumption
(SUTVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Propensity Scores - Confounding in Observational Studies . . . . . . . . . . 8
1.3.1 Calculating a Propensity Score . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Checking Covariate Balance and Evaluating Quality of Propensity
Score Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Propensity Score Adjustment . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Principle Stratication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1 Truncation Due to Death . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.2 Simplifying Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5 Sliding Dichotomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6 Prognostic Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Literature Review 27
2.1 Propensity Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Truncation Due to Death/Principle Stratication . . . . . . . . . . . . . . . 29
2.3 Prognostic Scores/Sliding Dichotomy . . . . . . . . . . . . . . . . . . . . . . 32
3 Confounding in Observational Studies: Comparing Propensity Score and
Traditional Regression Analyses 36
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Variance Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Methods - Pseudo-simulation . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5 Full Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Assessing Causal Eects with Truncation Due to Death and Missing
Mortality Status 72
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2 Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.1 Original Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Principle Stratication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.7 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7.1 Condence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7.2 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Prognostic Scores and Sliding Dichotomy 89
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Methods - Developing Predictive Models . . . . . . . . . . . . . . . . . . . . 94
5.4 Methods - Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Results - Sliding Dichotomy Power Analysis . . . . . . . . . . . . . . . . . . 103
5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.6.1 Power and Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.6.2 Traditional versus Alternative Predictive Models . . . . . . . . . . . 116
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.8 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Conclusions 119
Appendices 137
A Chapter 3 - Propensity Score 138
A.1 Theoretical Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2 Complete Pseudo-Simulation Results . . . . . . . . . . . . . . . . . . . . . . 139
A.3 Full Simulation Results - Marginal Mean . . . . . . . . . . . . . . . . . . . . 142
B Chapter 5 - Prognostic Scores and Sliding Dichotomy 145
B.1 Prognostic Score Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.2 Computer Code to Generate Sample Size Comparisons for Traditional and
Sliding Dichotomy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

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