Issues in Causal Inference and Applications to Public Health Public
Price, Megan Emily (2009)
Published
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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