Bayesian approach for proportional hazards mixture cure model allowing non-curable competing risk

With advancements in medical research, more and more diseases may be curable, which indicates some patients may not die of the disease of interest. Mixture cure models, which can capture patients being cured, attracts an increasing attention in practice. However, the existing mixture cure models only focused on the major event with a potential cure while ignoring the potential risk from other non-curable competing events, which are commonly seen in the real world. In this paper, we develop a Bayesian approach to estimate a proportional hazards mixture cure (PHMC) model allowing non-curable competing risk. Data augmentation method with latent binary cure indicators and event indicators are adopted to simplify the Markov chain Monte Carlo implementation. The baseline cumulative hazards for the PHMC model are formulated by counting processes with gamma process priors. Its performance is demonstrated through comprehensive simulation studies. Finally, the proposed method is applied to a prostate cancer clinical trial data set.