When the Ends do not Justify the Means: Learning Who is Predicted to Have Harmful Indirect Effects

There is a growing literature on finding rules by which to assign treatment based on an individual's characteristics such that a desired outcome under the intervention is maximized. A related goal entails identifying a subpopulation of individuals predicted to have a harmful indirect effect (the effect of treatment on an outcome through mediators), perhaps even in the presence of a predicted beneficial total treatment effect. In some cases, the implications of a likely harmful indirect effect may outweigh an anticipated beneficial total treatment effect, and would motivate further discussion of whether to treat identified individuals. We build on the mediation and optimal treatment rule literatures to propose a method of identifying a subgroup for which the treatment effect through the mediator is expected to be harmful. Our approach is nonparametric, incorporates post-treatment confounders of the mediator-outcome relationship, and does not make restrictions on the distribution of baseline covariates, mediating variables, or outcomes. We apply the proposed approach to identify a subgroup of boys in the MTO housing voucher experiment who are predicted to have a harmful indirect effect of housing voucher receipt on subsequent psychiatric disorder incidence through aspects of their school and neighborhood environments.