Bayesian Structured Hazard Regression

 

We present a class of nonparametric hazard rate regression models, including nonparametric, spatial and spatio-temporal components. The basic quantities in these models are multiplicative transition intensities that are specified by extending the Cox model with respect to several aspects often needed in applications: The traditional linear predictor is generalized to a structured additive predictor, with P-spline priors for log-baseline hazards, time-varying effects as well as non-linear effects of continous covariates or further time scales, and Markov random field or kriging priors for spatial effects. In addition, frailty terms may be included to account for unobserved heterogeneity. Inference can be conducted either fully Bayesian using Markov chain Monte Carlo simulation techniques or empirically Bayesian based on a mixed model representation.We discuss geoadditive survival models and multi-state-models, and illustrate methodology through several applications.

Joint work with Andrea Hennerfeind and Ludwig Fahrmeir.