Many biomedical studies collect data on times of occurrence for a health event that can occur 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 dynamic 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. Parametric 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 semiparametric 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.

Keywords: Breast cancer; Chemoprevention; Dirichlet process; Nonparametric Bayes; Palpable Tumors; Survival analysis; Tumor multiplicity data.

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