Doubly Robust Causal Inference

A Bayesian view of doubly robust causal inference

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both.In this paper, we explain in the framework of misspecified models why doubly robust inferences can not arise from purely likelihood-based arguments, and demonstrate this through simulations.As an alternative to bayesian propensity score analysis, we propose a bayesian posterior predictive approach for constructing doubly robust estimation procedures.Our approach appropriately decouples the outcome and treatment assignment models by incorporating the inverse treatment assignment probabilities in causal inferences as importanceance sampling weights in monte carlo integration.