Weighting-Based Sensitivity Analysis in Causal Mediation Studies

• In Event: New Methods and Applications in Causal Mediation: Identifying the Mechanisms Behind Intervention Outcomes

Abstract

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 general 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 identification assumptions and may jeopardize 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. In identifying the natural indirect effect, the selection bias due to omitted confounding of the mediator-outcome relationship is represented simply as the covariance between the weight discrepancy and the outcome in the experimental group; the selection bias in identifying the natural direct effect takes the opposite sign. The study provides an application example evaluating the impact of a Welfare-to-Work program on the psychological well-being of mothers with young children. A random assignment to the program would increase employment, which would in turn reduce maternal depression among welfare recipients. However, a lack of increase in employment after assignment to the program would instead intensify depression. Earlier research reported a negative indirect effect mediated by employment and a positive direct effect of the program on maternal depression. Applying the new weighting-based approach to sensitivity analysis, we find that these results are generally insensitive to the omission of potential pretreatment and posttreatment confounders. We conclude with a discussion of broad applications of this new approach to sensitivity analysis, which includes cases in which the treatment is not randomized. This study produced an R package for conducting the proposed sensitivity analysis procedure.

Authors

• Guanglei Hong, University of Chicago

• Xu Qin, University of Chicago

• Fan Yang, University of Chicago