Estimating Treatment Effects in a Principal Stratification Framework When Treatment Received Depends on a Key Covariate
Keywords: principal stratification, complier average causal effect (CACE), causal inference
Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. We investigate the role of a key covariate in identifying which patients belong to the latent principal stratum of “compliers” who could potentially receive either treatment and, adopting a Bayesian perspective, use a Gibbs sampler to compute estimates of the “complier average causal effect” (CACE). We apply the method to analyze a clinical trial comparing two treatments for jaw fractures, one surgical and the other a less expensive non-surgical procedure. A unique feature of the study protocol allowed surgeons to overrule the randomized treatment assignment. While surgeons’ exact rationale was not recorded, the data include a key covariate summarizing injury severity that could serve as proxy for the unrecorded rationale behind the surgeons’ treatment decisions. We address the possibility that using observed information on the injury severity covariate to model principal stratum membership induces differences between the treatment groups within the latent stratum of compliers.