  There is a growing literature on finding so-called optimal treatment rules,
which are rules by which to assign treatment to individuals based on an
individual's characteristics, such that a desired outcome is maximized. A
related goal entails identifying individuals who are predicted to have a
harmful indirect effect (the effect of treatment on an outcome through
mediators) even in the presence of an overall beneficial effect of the
treatment on the outcome. In some cases, the likelihood of a harmful indirect
effect may outweigh a likely beneficial overall effect, and would be reason to
caution against treatment for indicated individuals. We build on both the
current mediation and optimal treatment rule literature to propose a method of
identifying a subgroup for which the treatment effect through the mediator is
harmful. Our approach is nonparametric, incorporates post-treatment variables
that may confound the mediator-outcome relationship, and does not make
restrictions on the distribution of baseline covariates, mediating variables
(considered jointly), or outcomes. We apply the proposed approach to identify a
subgroup of boys in the Moving to Opportunity housing voucher experiment who
are predicted to have harmful indirect effects, though the average total effect
is beneficial.
