Optimal compliance prediction models for estimating causal effects

Abstract

Understanding the causal relationship between intervention and outcome is at the heart of most research in the health sciences, and a variety of statistical methods have been developed to address causality. However, noncompliance with treatment assignment is a key source of complication for causal inference. Estimation of causal effects is likely to be compounded by the presence of noncompliance in both treatment arms of clinical trials where the intention-to-treat (ITT) analysis produces 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 by stratifying the population into partially latent classes (principal strata) based on potential values observed after randomization (e.g. noncompliance) under each of the levels of randomized intervention. The present work combines the two strategies of model selection and principal stratification with a novel application to a real data from a trial conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy - HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. The causal model links the resulting two marginal prediction models with a user-defined sensitivity parameter which is a function of the correlation between the two compliance behaviours. The method's key assumption of conditional prediction is verified for our data via sensitivity analysis comparing results of causal estimates using different sets of predictors of compliance. We adjust for noncompliance in both treatment arms under a Bayesian framework to produce causal risk ratio estimates for each principal stratum. The results suggested better efficacy for HRT among those who would comply with it compared to those who would comply with either HRT or placebo: compliance with HRT treatment only and with either treatment allocation would reduce the risk for death (reinfarction) by 47%(25%) and 13%(60%) respectively.