Bayesian variable selection becomes more and more important in statistical analyses, in particular when performing variable selection in high dimensions. For survival time models and in the presence of genomic data, the state of the art is still quite unexploited. One of the more recent approaches suggests a Bayesian semiparametric proportional hazards model for right censored time-to-event data. We extend this model to directly include variable selection, based on a stochastic search procedure within a Markov chain Monte Carlo sampler for inference. This equips us with an intuitive and flexible approach and provides a way for integrating additional data sources and further extensions. We make use of the possibility of implementing parallel tempering to help improve the mixing of the Markov chains. In our examples, we use this Bayesian approach to integrate copy number variation data into a gene-expression-based survival prediction model. This is achieved by formulating an informed prior based on copy number variation. We perform a simulation study to investigate the model's behavior and prediction performance in different situations before applying it to a dataset of glioblastoma patients and evaluating the biological relevance of the findings.
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