A matching framework for truncation by death problems
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Even in a carefully designed randomized trial, outcomes for some study participants can be missing, or more precisely, ill-defined, because participants had died prior to date of outcome collection. This problem, known as truncation by death, means that the treated and untreated are no longer balanced with respect to covariates determining survival. To overcome this problem, researchers often utilize principal stratification and focus on the Survivor Average Causal Effect (SACE). The SACE is the average causal effect among the subpopulation that will survive regardless of treatment status. In this paper, we present a new approach based on matching for SACE identification and estimation. We provide an identification result for the SACE that motivates the use of matching to restore the balance among the survivors. We discuss various practical issues, including the choice of distance measures, possibility of matching with replacement, post-matching crude and model-based SACE estimators, and non-parametric tests. Our simulation results demonstrate the flexibility and advantages of our approach. Because the cross-world assumptions needed for SACE identification can be too strong and are unfalsifiable, we also present sensitivity analysis techniques and illustrate their use in real data analysis. Finally, a recent alternative for SACE that does not demand cross-world unfalsifiable assumptions targets the conditional separable effects. We show how our approach can also be utilized to estimate these causal effects.
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