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Motivated by a potential-outcomes perspective, the idea of principalstratification has been widely recognized for its relevance in settingssusceptible to posttreatment selection bias such as randomized clinical trialswhere treatment received can differ from treatment assigned. In one suchsetting, we address subtleties involved in inference for causal effects whenusing a key covariate to predict membership in latent principal strata. We showthat when treatment received can differ from treatment assigned in both studyarms, incorporating a stratum-predictive covariate can make estimates of the"complier average causal effect" (CACE) derive from observations in the twotreatment arms with different covariate distributions. Adopting a Bayesianperspective and using Markov chain Monte Carlo for computation, we developposterior checks that characterize the extent to which incorporating thepretreatment covariate endangers estimation of the CACE. We apply the method toanalyze a clinical trial comparing two treatments for jaw fractures in whichthe study protocol allowed surgeons to overrule both possible randomizedtreatment assignments based on their clinical judgment and the data contained akey covariate (injury severity) predictive of treatment received.

The potential for bias in principal causal effect estimation when treatment received depends on a key covariate