Robust inference on population indirect causal effects: the generalized front door criterion

Standard methods for inference about direct and indirect effects require stringent no‐unmeasured‐confounding assumptions which often fail to hold in practice, particularly in observational studies. The goal of the paper is to introduce a new form of indirect effect, the population intervention indirect effect, that can be non‐parametrically identified in the presence of an unmeasured common cause of exposure and outcome. This new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value. The population intervention indirect effect is in fact the indirect component of the population intervention effect, introduced by Hubbard and Van der Laan. Interestingly, our identification criterion generalizes Judea Pearl's front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable. For inference, we develop both parametric and semiparametric methods, including a novel doubly robust semiparametric locally efficient estimator, that perform very well in simulation studies. Finally, the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in Tanzania.