Causal Mediation Analysis with a Time-Dependent Mediator, Time-Dependent Confounders and a Time-to-Event Outcome: Revisiting the Difference Method

Mediation analysis is a powerful tool to decompose treatment effects into direct and indirect components, enabling explanations of total treatment effects in a formal statistical framework. However, applying such analyses to settings with time-to-event outcomes, time-dependent mediators and confounders remains challenging. Existing methods are statistically complex, computationally intensive, and rarely available in user-friendly software. The difference method offers a simple alternative, but its performance in this setting has not been systematically evaluated. We conducted a simulation study and real-world data analysis to fill this gap in the literature. Using Cox proportional hazards, Aalen additive hazards, and accelerated failure time (AFT) models with time-varying covariates, the difference method was compared across different data generation processes with time-dependent mediators and confounders, focusing on bias in estimated indirect effects. The parametric mediational g-formula was used as benchmark comparator. If correctly specified, the Aalen model based difference method produced unbiased estimates in the absence of a time-dependent confounder that was directly caused by the treatment. Similar results were obtained when using the Cox model based difference with rare outcomes, but not with common outcomes. The AFT model based difference method was biased in almost all scenarios, due to collapsibility issues. Only the parametric mediational g-formula was unbiased in all scenarios. In contrast to specialized methods, the difference method requires additional, often unrealistic, assumptions, such as the absence of a direct causal relationship of the treatment on time-dependent confounders. If those assumptions hold, however, it may be used as a simple and efficient alternative.