Heterogeneous interventional effects with multiple mediators: Semiparametric and nonparametric approaches

We propose semiparametric and nonparametric methods to estimate conditional interventional indirect effects in the setting of two discrete mediators whose causal ordering is unknown. Average interventional indirect effects have been shown to decompose an average treatment effect into a direct effect and interventional indirect effects that quantify effects of hypothetical interventions on mediator distributions. Yet these effects may be heterogeneous across the covariate distribution. We consider the problem of estimating these effects at particular points. We propose an influence function-based estimator of the projection of the conditional effects onto a working model, and show under some conditions that we can achieve root-n consistent and asymptotically normal estimates. Second, we propose a fully nonparametric approach to estimation and show the conditions where this approach can achieve oracle rates of convergence. Finally, we propose a sensitivity analysis that identifies bounds on both the average and conditional effects in the presence of mediator-outcome confounding. We show that the same methods easily extend to allow estimation of these bounds. We conclude by examining heterogeneous effects with respect to the effect of COVID-19 vaccinations on depression during February 2021.