Weighting-Based Sensitivity Analysis in Causal Mediation Studies

Through a sensitivity analysis, the analyst attempts to determine whether a conclusion of causal inference could be easily reversed by a plausible violation of an identification assumption. Analytic conclusions that are harder to alter by such a violation are expected to add a higher value to scientific knowledge about causality. This article presents a weighting-based approach to sensitivity analysis for causal mediation studies. Extending the ratio-of-mediator-probability weighting (RMPW) method for identifying natural indirect effect and natural direct effect, the new strategy assesses potential bias in the presence of omitted pretreatment or posttreatment covariates. Such omissions may undermine the causal validity of analytic conclusions. The weighting approach to sensitivity analysis reduces the reliance on functional form assumptions and removes constraints on the measurement scales for the mediator, the outcome, and the omitted covariates. In its essence, the discrepancy between a new weight that adjusts for an omitted confounder and an initial weight that omits the confounder captures the role of the confounder that contributes to the bias. The effect size of the bias due to omitted confounding of the mediator–outcome relationship is a product of two sensitivity parameters, one associated with the degree to which the omitted confounders predict the mediator and the other associated with the degree to which they predict the outcome. The article provides an application example and concludes with a discussion of broad applications of this new approach to sensitivity analysis. Online Supplemental Material includes R code for implementing the proposed sensitivity analysis procedure.