Bayesian piecewise mixture model for racial disparity in prostate cancer progression

Racial differences in prostate cancer incidence and mortality have been reported. Several authors hypothesize that African Americans have a more rapid growth rate of prostate cancer compared to Caucasians, that manifests in higher recurrence and lower survival rates in the former group. In this paper we propose a Bayesian piecewise mixture model to characterize PSA progression over time in African Americans and Caucasians, using follow-up serial PSA measurements after surgery. Each individual's PSA trajectory is hypothesized to have a latent phase immediately following surgery followed by a rapid increase in PSA indicating regrowth of the tumor. The true time of transition from the latent phase to the rapid growth phase is unknown, and can vary across individuals, suggesting a random change point across individuals. Furthermore, some patients may not experience the latent phase due to the cancer having already spread outside the prostate before undergoing surgery. We propose a two-component mixture model to accommodate patients both with and without a latent phase. Within the framework of this mixture model, patients who do not have a latent phase are allowed to have different rates of PSA rise; patients who have a latent phase are allowed to have different PSA trajectories, represented by subject-specific change points and rates of PSA rise before and after the change point. The proposed Bayesian methodology is implemented using Markov Chain Monte Carlo techniques. Model selection is performed using deviance information criteria based on the observed and complete likelihoods. Finally, we illustrate the methods using a prostate cancer dataset.