A Bayesian semiparametric partially PH model for clustered time‐to‐event data

A standard approach for dealing with unobserved heterogeneity and clustered time‐to‐event data within the proportional hazards (PH) context has been the introduction of a cluster‐specific random effect (frailty), common to subjects within the same cluster. However, the conditional PH assumption could be too strong for some applications. For example, the marginal association of survival functions within a cluster does not depend on the subject‐specific covariates. We propose an alternative partially PH modeling approach based on the introduction of cluster‐dependent random hazard functions and on the use of mixture models induced by completely random measures. The proposed approach accommodates for different degrees of association within a cluster, which varies as a function of cluster‐level and individual covariates. Moreover, a particular specification of the proposed model has the appealing property of preserving marginally the PH structure. We illustrate the performances of the proposed modeling approach on simulated and real data sets.