Cox's Proportional Hazards Model with Lp Penalty for Biomarker Identification and Survival Prediction

Advances in high throughput technology provide massive high dimensional data. It is very important and challenging to study the association of genes with various clinical outcomes. Due to large variability in time to certain clinical event among patients, studying possibly censored survival data can be more informative than classification. We proposed the Cox's proportional hazards model with Lp penalty method for simultaneous feature (gene) selection and survival prediction. Lp penalty shrinks coefficients and produces some coefficients that are exactly zero. It has been shown that Lp (p < 1) regularization performs better than L1 in the regression and classification framework (Knight & Fu 2000, Liu et al. 2007). Experimental results with different data demonstrate that the proposed procedures can be used for identifying important genes (features) that are related to time to death due to cancer and for building parsimonious model for predicting the survival of future patients.