Abstract: In many medical studies, an ultimate failure event, such as death, is likely to be affected by the occurrence and timing of other intermediate clinical events. Both event times are subject to censoring by loss-to-follow-up, but the nonterminal event may be further censored by the occurrence of the primary outcome, but not vice versa. To study the effect of an intervention on both events, the intermediate event may be viewed as a mediator. However, the conventional definitions of direct and indirect effects do not apply, because of the semi-competing risks data structure. We define three principal strata based on whether the potential intermediate event occurs before the potential failure event. This allows us to properly define direct and indirect effects in one stratum, and define total effects for all strata. We discuss the identification conditions for the stratum-specific effects, and propose a semiparametric estimator based on a multivariate logistic stratum membership model and within-stratum proportional hazards models for the event times. By treating the unobserved stratum membership as a latent variable, we propose an expectation-maximization algorithm for the computation. We study the asymptotic properties of the estimators using modern empirical process theory and examine the performance of the estimators in numerical studies.

Key words and phrases: Illness-death model, missing data, principal stratification, proportional hazards model, survival analysis.