A Bayesian Approach to Estimate Causal Average Treatment Effects Under Unmeasured Confounding.

One major bias source in causal inference for clinical trials is unmeasured confounding. We propose an innovative, practical Bayesian modeling approach to adjust for unmeasured confounding effects and obtain precise causal average treatment effect estimates for two-arm randomized controlled clinical trials. This approach includes model reparameterization and an iterative algorithm, with a causal inference framework incorporated with unmeasured confounders and related statistical distributions. Model non-identifiability resulting from adjusting for unmeasured confounding is a major inferential problem. Reparameterization transforms one or multiple unmeasured confounders into a single reparameterized unmeasured confounder and can remove model non-identifiability from the model specification of unmeasured confounders. The iterative algorithm consists of detailed steps for inference after model reparameterization and can remove model non-identifiability from prior sensitivity to unmeasured confounders. It includes iterating the prior distribution of the reparameterized unmeasured confounder by certain rules, aggregating posterior means and variances over different prior choices, and obtaining posterior estimates for the average treatment effect. Its essential idea is to make unreliable prior information on unmeasured confounders as close to data information as possible. Compared with usual methods, our approach produces robust effect estimates and correctly concludes statistical significance. From an example using real clinical data, this approach effectively adjusts for confounding effects when we do not adjust for measured confounders. Our approach is also generalizable to other clinical study designs and may be beneficial to applications where data collection is difficult for certain variables or causal relationships are not well understood.