Bayesian semiparametric dynamic frailty models for multiple event time data

Many biomedical studies collect data on times of occurrence for a health event that can oc-cur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dy-namic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating non-proportional hazards. Paramet-ric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semipara-metric model on a conditionally-conjugate dynamic gamma model, we facilitate posterior computation and lack of fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study