On Identification and Inference for Direct Effects

Consider the query: Does a binary treatment X have a causal effect on a response Y through a causal pathway that does not involve the intermediate variable M? This query is often rephrased as: Does X have a direct causal effect on Y not through M? Direct effects have been formally defined in three different ways: the controlled direct effects (CDE), the natural direct effects (i.e. pure and total direct effects PDE and TDE), and the principal stratum direct effects (PSDE). In this issue of the journal, Hafeman and VanderWeele (H&V) 7 provide novel minimal or near minimal conditions for identification of the CDE, PDE and TDE but do not consider the PSDE. In this commentary, we review inference for direct effects and the results of H&V. We also review the close relationship between the direct effects literature and the literature on instrumental variables and Mendelian randomization.