Estimation of controlled direct effects in time-varying treatments using structural nested mean models: application to a primary prevention trial for coronary events with pravastatin

Abstract

For the estimation of controlled direct effects (i.e., direct effects controlling intermediates that are set at a fixed level for all members of the population) without bias, two fundamental assumptions must hold: the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome. Even if these assumptions hold, one would nonetheless fail to estimate direct effects using standard methods, for example, stratification or regression modeling, when the treatment influences confounding factors. For such situations, the sequential g-estimation method for structural nested mean models has been developed for estimating controlled direct effects in point-treatment situations. In this study, we demonstrate that this method can be applied to longitudinal data with time-varying treatments and repeatedly measured intermediate variables. We sequentially estimate the parameters in two structural nested mean models: one for a repeatedly measured intermediate and the other one for direct effects of a time-varying treatment. The method was applied to data from a large primary prevention trial for coronary events, in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia.

Keywords: causal inference; direct effects; longitudinal data; structural nested mean model; time-dependent confounding.