Accelerated failure time models for semi‐competing risks data in the presence of complex censoring

Statistical analyses that investigate risk factors for Alzheimer's disease (AD) are often subject to a number of challenges. Some of these challenges arise due to practical considerations regarding data collection such that the observation of AD events is subject to complex censoring including left‐truncation and either interval or right‐censoring. Additional challenges arise due to the fact that study participants under investigation are often subject to competing forces, most notably death, that may not be independent of AD. Towards resolving the latter, researchers may choose to embed the study of AD within the “semi‐competing risks” framework for which the recent statistical literature has seen a number of advances including for the so‐called illness‐death model. To the best of our knowledge, however, the semi‐competing risks literature has not fully considered analyses in contexts with complex censoring, as in studies of AD. This is particularly the case when interest lies with the accelerated failure time (AFT) model, an alternative to the traditional multiplicative Cox model that places emphasis away from the hazard function. In this article, we outline a new Bayesian framework for estimation/inference of an AFT illness‐death model for semi‐competing risks data subject to complex censoring. An efficient computational algorithm that gives researchers the flexibility to adopt either a fully parametric or a semi‐parametric model specification is developed and implemented. The proposed methods are motivated by and illustrated with an analysis of data from the Adult Changes in Thought study, an on‐going community‐based prospective study of incident AD in western Washington State.