Summary
Methods based on the propensity score comprise one set of valuable tools for comparative effectiveness research and for estimating causal effects more generally. These methods typically consist of two distinct stages: 1) a propensity score stage where a model is fit to predict the propensity to receive treatment (the propensity score), and 2) an outcome stage where responses are compared in treated and untreated units having similar values of the estimated propensity score. Traditional techniques conduct estimation in these two stages separately; estimates from the first stage are treated as fixed and known for use in the second stage. Bayesian methods have natural appeal in these settings because separate likelihoods for the two stages can be combined into a single joint likelihood, with estimation of the two stages carried out simultaneously. One key feature of joint estimation in this context is “feedback” between the outcome stage and the propensity score stage, meaning that quantities in a model for the outcome contribute information to posterior distributions of quantities in the model for the propensity score. We provide a rigorous assessment of Bayesian propensity score estimation to show that model feedback can produce poor estimates of causal effects absent strategies that augment propensity score adjustment with adjustment for individual covariates. We illustrate this phenomenon with a simulation study and with a comparative effectiveness investigation of carotid artery stenting vs. carotid endarterectomy among 123,286 Medicare beneficiaries hospitlized for stroke in
Over the last two decades, statistics educators have made important changes to introductory courses. Current guidelines emphasize developing statistical thinking in students and exposing them to the entire investigative process in the context of interesting research questions and real data. As a result, many concepts (confounding, multivariable models, study design, etc.) previously reserved only for higherlevel courses now appear in introductory courses. Despite these changes, causality is rarely discussed in introductory courses, except for warning students "correlation does not imply causation" or covering the special case of randomized controlled experiments. In this article, we argue causal inference concepts align well with statistics education guidelines for introductory courses by developing statistical and multivariable thinking, exposing students to many aspects of the investigative process, and fostering active learning. We discuss how to integrate causal inference concepts into introductory courses using causal diagrams and provide an illustrative example with youth smoking data. Through our website, we also provide a guided student activity and instructor resources. Supplementary materials for this article are available online.
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