Bayesian cure-rate survival model with spatially structured censoring

Abstract

We propose a Bayesian spatial model for time-to-event data in which we allow the censoring mechanism to depend on covariates and have a spatial structure. The survival model incorporates a cure rate fraction and assumes that the time-to-event follows a Weibull distribution, with covariates such as race, stage, grade, marital status and age at diagnosis being linked to its scale parameter. With right censoring being a primary concern, we consider a joint logistic regression model for the death versus censoring indicator, allowing dependence on covariates and including a spatial structure via the use of random effects. We apply the models to examine prostate cancer data from the Surveillance, Epidemiology, and End Results (SEER) registry, which displays marked spatial variation.

Keywords: Bayesian hierarchical models; Markov chain Monte Carlo; cure rate; prostate cancer; spatial analysis.

Figure 1.

Map of random effects: A) map of uncorrelated random effects in the main model; B) map of uncorrelated random effects in the censoring model.

Figure 2.

Map of random effects: A) map of uncorrelated random effects, simulated data model 1 UH; B)map of uncorrelated random effects in the censoring model, simulated data model 1, UH; C) map of sum of uncorrelated and correlated random effects, simulated data model 1 UH+CH; D) map of sum of uncorrelated and correlated random effects in the censoring model, simulated data model 1 UH+CH; E) map of spatially correlated covariate.