Approximate Bayesian Bootstrap procedures to estimate multilevel treatment effects in observational studies with application to type 2 diabetes treatment regimens.

Randomized clinical trials are considered as the gold standard for estimating causal effects. Nevertheless, in studies that are aimed at examining adverse effects of interventions, randomized trials are often impractical because of ethical and financial considerations. In observational studies, matching on the generalized propensity scores was proposed as a possible solution to estimate the treatment effects of multiple interventions. However, the derivation of point and interval estimates for these matching procedures can become complex with non-continuous or censored outcomes. We propose a novel Approximate Bayesian Bootstrap algorithm that results in statistically valid point and interval estimates of the treatment effects with categorical outcomes. The procedure relies on the estimated generalized propensity scores and multiply imputes the unobserved potential outcomes for each unit. In addition, we describe a corresponding interpretable sensitivity analysis to examine the unconfoundedness assumption. We apply this approach to examine the cardiovascular safety of common, real-world anti-diabetic treatment regimens for type 2 diabetes mellitus in a large observational database.