Bayesian doubly robust estimation of causal effects for clustered observational data.

Observational data often exhibit clustered structure, which leads to inaccurate estimates of exposure effect if such structure is ignored. To overcome the challenges of modelling the complex confounder effects in clustered data, we propose a Bayesian doubly robust estimator of causal effects with random intercept BART to enhance the robustness against model misspecification. The proposed approach incorporates the uncertainty in the estimation of the propensity score, potential outcomes and the distribution of individual-level and cluster-level confounders into the exposure effect estimation, thereby improving the coverage probability of interval estimation. We evaluate the proposed method in the simulation study compared with frequentist doubly robust estimators with parametric and nonparametric multilevel modelling strategies. The proposed method is applied to estimate the effect of limited food access on the mortality of cardiovascular disease in the senior population.