Causal Inference with Selection and Confounding Variables
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Most complex observational and randomized studies are motivated by the potential of drawing causal statements. However, a usual statistical analysis may yield estimates that do not have causal interpretations. In fact, unlike most other parameters, identification of causal parameters usually relies on untestable assumptions. Moreover, even under these identification assumptions, estimation of causal parameters often relies on nuisance models. The parameter estimation in the nuisance models is crucial to obtain robust causal effect estimates. My research attempts to address these methodological hallenges. In Chapter 2 we study robust estimation of propensity score weights. The propensity score plays a central role in inferring causal effects from observational studies. In particular, weighting and subclassification are two principal approaches to estimate the average causal effect based on estimated propensity scores. Unlike the conventional version of the propensity score subclassification estimator, if the propensity score model is correctly specified, the weighting methods offer consistent and possibly efficient estimation of the average causal effect. However, this theoretical appeal may be diminished in practice by sensitivity to misspecification of the propensity score model. In contrast, subclassification methods are usually more robust to model misspecification. We hence propose to use subclassification for robust estimation of propensity score weights. Our approach is based on the intuition that the inverse probability weighting estimator can be seen as the limit of subclassification estimators as the number of subclasses goes to infinity. By formalizing this intuition, we propose novel propensity score weighting estimators that are both consistent and robust to model misspecification. Empirical studies show that the proposed estimators perform favorably compared to existing methods. In Chapter 3 we study identification and estimation of causal effects with outcomes truncated by death. It is common that in medical studies, the outcome of interest is truncated by death, meaning that a subject had died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. It is hence of interest to estimate the survivor average causal effect (SACE), defined as the average causal effect among subjects who would survive under either exposure. In this chapter, we consider the identification and estimation problems of the SACE. We propose to identify a substitution variable for the latent membership of the always-survivor group. The identifiability conditions required for a substitution variable are similar in idea to conditions for an instrumental variable. We show that the SACE is identifiable with use of a substitution variable, and propose novel model parameterizations for estimation of the SACE under our identification assumptions. Our approaches are illustrated via simulation studies and two data analyses. In Chapter 4, we study causal analysis of ordinal treatments and binary outcomes under truncation by death. It is common that in multi-arm randomized trials, the outcome of interest is “truncated by death,” meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts.
- Biostatistics