Bayesian semiparametric model for spatially correlated interval-censored survival data

Interval-censored survival data are often recorded in medical practice. Although some methods have been developed for analyzing such data, issues still remain in terms of efficiency and accuracy in estimation. In addition, interval-censored data with spatial correlation are not unusual but less studied. In this paper, we propose an efficient Bayesian approach under a proportional hazards frailty model to analyze interval-censored survival data with spatial correlation. Specifically, a linear combination of monotonic splines is used to model the unknown baseline cumulative hazard function, leading to a finite number of parameters to estimate while maintaining adequate modeling flexibility. A conditional autoregressive distribution is employed to model the spatial dependency. A two-step data augmentation through Poisson latent variables is used to facilitate the computation of posterior distributions that are essential in the proposed MCMC algorithm. Simulation studies are conducted to evaluate the performance of the proposed method. The approach is illustrated through geographically referenced smoking cessation data in southeastern Minnesota where time to relapse is modeled and spatial structure is examined.