Nonparametric Bayesian modeling for hazard functions in spatial survival data

Abstract

Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs. The Cox proportional hazard is the most widely used in survival analysis as it takes advantage that it accounts for the proportionate risk of covariates without estimating baseline hazards. However, it is necessary to obtain the baseline hazard function as well as regression parameters to describe the exact hazards of a study population. When data is collected by clinical sites or geographical regions, we should reflect the spatial structures into the model. In this paper we adopted a nonparametric Bayesian hierarchical model to estimate the hazard function in spatial survival data. We assume the cumulative baseline hazard function as a monotone step function, considering flexible priors called stick-breaking priors. We provide modeling for the hazard function that can describe spatial structure, and apply it to survival data which is observed in 24 administrative districts in the northwest of England.