Sensitivity Analysis for Pretreatment Confounding With Multiple Mediators

The causal mediation literature has developed techniques to assess the sensitivity of an inference to pretreatment confounding, but these techniques are limited to the case of a single mediator. In this article, we extend sensitivity analysis to possible violations of pretreatment confounding in the case of multiple mediators. In particular, we develop sensitivity analyses under three alternative approaches to effect decomposition: (1) jointly considered mediators, (2) identifiable direct and indirect paths, and (3) interventional analogues effects. With reasonable assumptions, each approach reduces to a single procedure to assess sensitivity in the presence of simultaneous pre- and posttreatment confounding. We demonstrate our sensitivity analysis techniques with a framing experiment that examines whether anxiety mediates respondents’ attitudes toward immigration in response to an information prompt.