Classification of pathological stage of prostate cancer patients using penalized splines

We propose a penalized splines (P-splines) based method to predict the pathological stage of localized prostate cancer. A combination of prostate-specific antigen, Gleason histological score, and clinical stage from a cohort study of 834 prostate cancer patients are used to build the P-splines model. It turns out that the proposed methodology results in improved prediction of pathological stage compared to usual logistic regression after removing a few outliers. The improvement is shown to be statistically significant. Receiver-operating characteristic (ROC) curve is drawn and we show that the increase in area under the ROC curve over the commonly used logistic regression based classification method is also statistically significant.