Threshold Gradient Descent Regularization in the Additive Risk Model with High-Dimensional Covariates

An additive risk model is a useful alternative to the Cox model (Cox, 1972) and may be adopted when the absolute effects, instead of the relative effects, of multiple predictors on the hazard function are of interest. In this article, we propose using the threshold gradient descent regularization (TGDR) method for covariate selection, estimation and prediction in the additive risk model for right censored survival data when the dimension of the covariate vector can be greater than the sample size. Such " small n, large p " problems may arise in the investigation of association between survival times and gene expression profiles. We propose using the V-fold cross validation and a modified Akaike's Information Criterion (AIC) for tuning parameter selections. The proposed method is demonstrated with two real data examples. The results show that the TGDR is effective in model reduction and can identify more relevant covariates than the least absolute shrinkage and selection operator approach.