Multiply robust Bayesian procedures for causal inference problems

Observational studies are common in epidemiology, medicine, economics, and other research fields. Causal inference has been regarded as one of the most effective tools for conducting statistical inference with observational studies without random treatment assignments. The validity of most existing causal inference procedures depends on the underlying outcome regression and/or propensity score modeling assumptions. In this paper, we propose two new Bayesian multiply robust estimation approaches for causal inference based on the loss-likelihood bootstrap. The proposed methods enjoy the multiple robustness property such that the estimators of treatment effect are consistent if at least one of the outcome regression models or propensity score models is correctly specified. Convenient statistical inference can be conducted using the Bayesian posterior credible intervals. A simulation study shows the benefits of our proposed methods. We further apply our proposed methods by using 2009-2010 National Health and Nutrition Examination Survey (NHANES) data to examine the effect of exposure to perfluoroalkyl acids (PFAs) on kidney function.