Existing methods in causal inference do not account for the uncertainty in the selection of confounders. We propose a new class of estimators for the average causal effect, the model averaged double robust estimators, that formally account for model uncertainty in both the propensity score and outcome model through the use of Bayesian model averaging. These estimators build on the desirable double robustness property by only requiring the true propensity score model or the true outcome model be within a specified class of models to maintain consistency. We provide asymptotic results and conduct a large scale simulation study that indicates the model averaged double robust estimator has better finite sample behavior than the usual double robust estimator.
Cefalu, Matthew; Dominici, Francesca; and Parmigiani, Giovanni, "Model Averaged Double Robust Estimation" (February 2013). Harvard University Biostatistics Working Paper Series. Working Paper 149.