Bayesian analysis of doubly semiparametric mixture cure models with interval-censored data

Abstract

Interval-censored data are commonly encountered in medical studies, where the occurrence of a disease can only be observed within specific time intervals or during periodic examinations. In the presence of individuals being cured or never experiencing the disease, a mixture cure model is often assumed for regression analysis accounting for the mixture of cured and uncured individuals in the study population. In this model, the Cox proportional hazards model is typically specified as a latency component for the event time and logistic regression as an incidence component for the probability of uncured. Challenges appear in the analysis when some covariates are time-related. It is unrealistic to assume linear covariate effects on a known transformation of cure probability or the hazard ratio of uncured individuals, as is commonly done. We propose a doubly semiparametric mixture cure model for interval-censored data, providing more flexibility by allowing linear and nonlinear effects of covariates in both the incidence and latency parts. We develop a computationally feasible Bayesian estimation procedure, incorporating a two-stage data augmentation with Poisson latent variables to deal with interval-censored data and splines for modelling the nonlinear terms in the model. We evaluate the finite sample performance of the proposed method via extensive simulations and demonstrate its utility through analysis of data from a hypobaric decompression sickness study.