Mediation analysis in longitudinal intervention studies with an ordinal treatment-dependent confounder.

In interventional health studies, causal mediation analysis can be employed to investigate mechanisms through which the intervention affects the targeted health outcome. Identifying direct and indirect effects from empirical data become complicated, however, when a confounder of the mediator-outcome association is itself affected by the treatment. Here, we investigate identification of mediational effects under such post-treatment confounding in a setting with a longitudinal mediator, time-to-event outcome and an ordinal treatment-dependent confounder. If the treatment affects the treatment-dependent confounder only in one direction (monotonicity), we show that the mediational effects are identified up to stratum-specific sensitivity parameters and derive their empirical non-parametric expressions. The feasibility of the monotonicity assumption can be assessed using empirical data, based on restrictions on the marginal distributions of counterfactuals of the treatment-dependent confounder. In an empirical analysis, we use data from the Finnish Diabetes Prevention Study to assess the extent to which the effect of a lifestyle intervention on avoiding type 2 diabetes is mediated through weight reduction in a high-risk population, with other health-related changes acting as treatment-dependent confounders. We avoid pitfalls related to post-treatment conditioning by treating the mediator as a functional entity and defining the time-to-event outcome as a restricted disease-free time.