The generalized front-door criterion for estimation of indirect causal effects of a confounded treatment
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The population intervention effect (PIE) of an exposure measures the expected change of an outcome from its observed value, if one intervened to withhold the exposure in the entire population. This effect is of interest when evaluating the potential impact of programs that eliminate a harmful exposure from a population. The goal of this paper is to develop methodology to identify and estimate the indirect component of the PIE; that is, the extent to which the exposure affects the outcome through an intermediate variable in a setting where the exposure-outcome relation may be subject to unmeasured confounding. The conditions to empirically identify this population intervention indirect effect are shown to be a generalization of Pearl's front-door criterion. Although Pearl's front-door recovers the indirect effect when exposure is confounded, it relies on the stringent assumption of no direct effect of exposure not captured by the intermediate variable. The generalized front-door relaxes this assumption. Both parametric and semiparametric doubly robust and locally efficient estimators of the population intervention indirect effect are proposed and evaluated in a simulation study. Finally, these methods are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health program in Tanzania.
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