A Bayesian proportional hazards mixture cure model for partly interval-censored data

Time-to-event data with a cure fraction are frequently encountered in medical field. Many cure models have been developed for right-censored data and even for interval-censored data. However, the work of cure model for partly interval-censored data is very limited. In this article, we propose a two-component mixture cure model for partly interval-censored data with a cure fraction under the Bayesian semiparametric setting. The incidence part is modeled using a logistic regression model and the latency part is modeled using a proportional hazards model. We examine the performance of the proposed method through extensive simulation studies and also compare it to two methods currently available in the literature but under the frequentist framework. The use of the proposed method is illustrated through analyzing a data set of childhood mortality from the 2003 Nigeria Demographic and Health Survey.