Applying optimal model selection in principal stratification for causal inference

Noncompliance to treatment allocation is a key source of complication for causal inference. Efficacy estimation is likely to be compounded by the presence of noncompliance in both treatment arms of clinical trials where the intention-to-treat estimate provides a biased estimator for the true causal estimate even under homogeneous treatment effects assumption. Principal stratification method has been developed to address such posttreatment complications. The present work extends a principal stratification method that adjusts for noncompliance in two-treatment arms trials by developing model selection for covariates predicting compliance to treatment in each arm. We apply the method to analyse data from the Esprit study, which was conducted to ascertain whether unopposed oestrogen (hormone replacement therapy) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We adjust for noncompliance in both treatment arms under a Bayesian framework to produce causal risk ratio estimates for each principal stratum. For mild values of a sensitivity parameter and using separate predictors of compliance in each arm, principal stratification results suggested that compliance with hormone replacement therapy only would reduce the risk for death and myocardial reinfarction by about 47% and 25%, respectively, whereas compliance with either treatment would reduce the risk for death by 13% and reinfarction by 60% among the most compliant. However, the results were sensitive to the user-defined sensitivity parameter.