LAUSR

We congratulate Dr. Huang for his contribution to tackle an important yet underexplored problem. The problemhas numerous potential applications inmedical researchwhen both the primary and intermediate outcomes are event times, but the presence of a time-to-event “mediator” poses unique challenges in generalizing existing causal mediation methods that often assume a well-defined mediator right after the treatment is being assigned.Dr.Huang beautifully formulates the estimation problem in a weighted counting process framework with weights adaptive to the filtration generated by the counting processes, so that the powerful machinery of martingale leads to asymptotic results with simple estimators of asymptotic variances. In this discussion, we will first discuss the reasons why we think this problem is difficult. Then, we offer some reflections on the conceptual framework and assumptions given in this paper, and offer alternative interpretations of the estimands.