Geoadditive survival models

Survival data often contain geographical or spatial information,
such as the residence of individuals. We propose geoadditive
survival models for analyzing spatial effects jointly with possibly
nonlinear effects of other covariates. Within a unified Bayesian
framework, our approach extends the classical Cox model to a more
general multiplicative hazard rate model, augmenting the common
linear predictor with a spatial component and nonparametric terms
for nonlinear effects of time and metrical covariates. Markov
random fields and penalized regression splines are used as basic
building blocks. Inference is fully Bayesian and uses
computationally efficient MCMC sampling schemes. Smoothing
parameters are an integral part of the model and are estimated
automatically. Perfomance is investigated through simulation
studies. We apply our approach to data from a case study in London
and Essex that aims to estimate the effect of area of residence and
further covariates on waiting times to coronary artery bypass graft
(CABG).