Hennerfeind, Andrea; Brezger, Andreas; Fahrmeir, Ludwig
Geoadditive survival models.
Collaborative Research Center 386, Discussion Paper 333
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).