Practical properties of some structural mean analyses of the effect of compliance in randomized trials

We can use the structural mean model (SMM) to estimate the mean effect of dose-timing patterns of active treatment actually taken by patients in a randomized placebo-controlled trial. An SMM therefore models the expected difference between a patient's potential response on the treatment arm and potential response on the placebo arm as a function of observed compliance on the treatment arm and baseline predictors. It accounts for the possibly selective nature of noncompliance without needing to model that aspect directly. It nevertheless enjoys the intention-to-treat property of protecting the alpha level when we are testing the hypothesis of no treatment effect. In the presence of selective compliance, classical regression methods lead to inconsistent and seriously biased estimates of the effects of treatment actually taken. The SMM is designed to reduce these problems. This paper studies selectivity and addresses some practical properties of the SMM estimator. Specifically, we use a blood pressure trial to explore the precision of the estimates in practical cases. We also compare mean squared errors (MSEs) of an SMM and the ordinary least-squares (OLS) estimator. We study the effect of baseline covariates on the precision of the SMM estimator and describe the potential role of a run-in period in this regard.