Statistical Considerations for Clinical Trials During COVID-19: Natural History Controls for Survival Analysis (Part III)

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For observational studies, the propensity score is the probability of treatment for a given set of baseline covariates. Rosenbaum and Rubin (1983) propose use of a propensity score to pre-process risk factors for causal inference. Four inferential approaches using the propensity score for causal inference are propensity score matching (PSM), stratification based on propensity score percentiles (e.g., quintiles), covariate adjustment using the propensity score, and inverse probability treatment weighting (IPTW). These methods rely on the property that conditional on the propensity score, treatment status is independent of baseline covariates, and thus, causal inference involving multi-dimensional covariates reduces to analysis conditional on one-dimensional propensity score. The idea that a one-dimensional score could contain information in multi-dimensional covariates is counter intuitive. Specific information contained in the covariates has to be lost in the dimension reduction process of computing the propensity score. In the 2019 paper published in Political Analysis by Cambridge University Press entitled “Why Propensity Scores Should Not Be Used for Matching”, King and Nielsen state that propensity score matching (PSM)