Abstract: Structural mean models were developed to estimate average treatment effects in function of received exposures and baseline covariates. Recent extensions allow treatment effects to vary additionally with subjects' potential response to a treatment-free regime. This makes it possible to investigate in clinical trials, for instance, how well drug action is predicted by patients' natural health status in the absence of treatment. Accommodating this is challenging, however, because treatment activity and potential treatment-free response are (usually) unobservable for subjects on treatment.
In this paper, we model and estimate the effect of treatment-free outcomes on treatment activity in randomized controlled clinical trials with measured compliance. Our purpose is (a) to enhance modelling flexibility over existing approaches; and (b) to investigate to what extent the identification of such effects relies on untestable modelling assumptions. We develop new classes of estimators for this effect that make better use of the information in the data and achieve greater robustness to model misspecification. The new methods are evaluated by large sample approximation and a simulation study.
Key words and phrases: Causal inference, noncompliance, structural models.