Improving medical predictive models via Likelihood Gamble Pricing

A combination of radiotherapy and chemotherapy, is often the treatment of choice for cancer patients. Recent develop- ments in the treatment of patients have lead to improved survival. However, traditionally used clinical variables have poor accuracy for the prediction of survival and radiation treatment side effects. The objective of this work is to develop and validate improved predictive model for a large group of non- small cell lung cancer (NSCLC) patients and a group of rectal cancer patients. The main goal is to predict survival for both groups of patients and radiation induced side-effects for the NSCLC patients. Given sufficiently accurate predictions of these models, they can then be used to optimize the treatment of each individual patient, which is the goal of personalized medicine. Our improved predictive models are obtained by using the recently proposed Likelihood gamble pricing (LGP), which is a decision-theoretic approach to statistical inference that marries the likelihood principle of statistics with Von Neumann-Morgensterns axiomatic approach to decision making. The regularization induced by the LPG approach produces better probabilistic predictions than both the unregularized and the regularized (by the standard 2-norm regularization) widely used logistic regression approaches.