Sensitivity analyses for parametric causal mediation effect estimation

Causal mediation analysis uses a potential outcomes framework to estimate the direct effect of an exposure on an outcome and its indirect effect through an intermediate variable (or mediator). Causal interpretations of these effects typically rely on sequential ignorability. Because this assumption is not empirically testable, it is important to conduct sensitivity analyses. Sensitivity analyses so far offered for this situation have either focused on the case where the outcome follows a linear model or involve nonparametric or semiparametric models. We propose alternative approaches that are suitable for responses following generalized linear models. The first approach uses a Gaussian copula model involving latent versions of the mediator and the final outcome. The second approach uses a so-called hybrid causal-observational model that extends the association model for the final outcome, providing a novel sensitivity parameter. These models, while still assuming a randomized exposure, allow for unobserved (as well as observed) mediator-outcome confounders that are not affected by exposure. The methods are applied to data from a study of the effect of mother education on dental caries in adolescence.