We establish the extent to which predictions of recurrence of prostate cancer (relapse) taken using preoperative biomarkers could be improved upon using Bayesian methodology. We analyse thedataset of Shariat et al to compare the improvement in prediction of relapse times using biomarkers with models which omitthem. Using half the dataset for training and the other half for testing, predictions of relapse time by a Bayesian approach using a skew-Student mixture model are compared to those using the traditional Cox model. The predictions from the Bayesian model are found to outperform those of the Cox model but the overall yield of predictive information leaves plenty of scope for improvement in the range of biomarkers in use. The Bayesian model presented here is the first such model for prostate cancer to consider the variation of relapse hazard with biomarker concentrations to be smooth, as is intuitively believable. It is also the first model to be shown to provide improved quality of prediction over the Cox model and indeed the first to be shown to provide positive apparent Shannon information relative to an exponential prior.
