Threshold gradient descent method for censored data regression with applications in pharmacogenomics

An important area of research in pharmacogenomics is to relate high-dimensional genetic or genomic data to various clinical phenotypes of patients. Due to large variability in time to certain clinical event among patients, studying possibly censored survival phenotypes can be more informative than treating the phenotypes as categorical variables. In this paper, we develop a threshold gradient descent (TGD) method for the Cox model to select genes that are relevant to patients' survival and to build a predictive model for the risk of a future patient. The computational difficulty associated with the estimation in the high-dimensional and low-sample size settings can be efficiently solved by the gradient descent iterations. Results from application to real data set on predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed method can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. The TGD based Cox regression gives better predictive performance than the L2 penalized regression and can select more relevant genes than the L1 penalized regression.