Direct effect models

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is not mediated by an intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Robins, Greenland and Pearl develop counterfactual definitions for two types of direct effects, natural and controlled, and discuss assumptions, beyond those of sequential randomization, required for the identifiability of natural direct effects. Building on their earlier work and that of others, this article provides an alternative counterfactual definition of a natural direct effect, the identifiability of which is based only on the assumption of sequential randomization. In addition, a novel approach to direct effect estimation is presented, based on assuming a model directly on the natural direct effect, possibly conditional on a subset of the baseline covariates. Inverse probability of censoring weighted estimators, double robust inverse probability of censoring weighted estimators, likelihood-based estimators, and targeted maximum likelihood-based estimators are proposed for the unknown parameters of this novel causal model.