Ratio of Mediator Probability Weighting for Estimating Natural Direct and Indirect Effects

Decomposing a total causal effect into natural direct and indirect effects is central to revealing causal mechanisms. Conventional methods achieve the decomposition by specifying an outcome model as a linear function of the treatment, the mediator, and the observed covariates under identification assumptions including the assumption of no interaction between treatment and mediator. Recent statistical advances relax this assumption typically within the linear or nonlinear regression framework with few exceptions. I propose a non-parametric approach that also relaxes the assumption of no treatment-mediator interaction while avoiding the problems of outcome model specification that become particularly acute in the presence of a large number of covariates. The key idea is to estimate the marginal mean of each counterfactual outcome by weighting every experimental unit such that the weighted distribution of the mediator under the experimental condition approximates their counterfactual mediator distribution under the control condition. The weight to be applied for this purpose is a ratio of the conditional probability of a mediator value under the control condition to the conditional probability of the same mediator value under the experimental condition. A nonparametric approach to estimating the weight on the basis of propensity score stratification promises to increase the robustness of the direct and indirect effect estimates. The outcome is modeled as a function of the direct and indirect effects with minimal model-based assumptions. In contrast with the regression-based approaches, this new method applies regardless of the distribution of the outcome or the functional relationship between the outcome and the mediator, and is suitable for handling a large number of pretreatment covariates. Under modified identification assumptions, the weighting method also makes adjustment for post-treatment covariates, a benefit apparently unavailable in the existing methods.