Spatial extended hazard model with application to prostate cancer survival

Summary This article develops a Bayesian semiparametric approach to the extended hazard model, with generalization to high‐dimensional spatially grouped data. County‐level spatial correlation is accommodated marginally through the normal transformation model of Li and Lin (2006, Journal of the American Statistical Association 101 , 591–603), using a correlation structure implied by an intrinsic conditionally autoregressive prior. Efficient Markov chain Monte Carlo algorithms are developed, especially applicable to fitting very large, highly censored areal survival data sets. Per‐variable tests for proportional hazards, accelerated failure time, and accelerated hazards are efficiently carried out with and without spatial correlation through Bayes factors. The resulting reduced, interpretable spatial models can fit significantly better than a standard additive Cox model with spatial frailties.