Tuning Parameter Selection in Cox Proportional Hazards Model with a Diverging Number of Parameters

Scand Stat Theory Appl. 2018 Sep;45(3):557-570. doi: 10.1111/sjos.12313. Epub 2018 Jan 16.

Abstract

Regularized variable selection is a powerful tool for identifying the true regression model from a large number of candidates by applying penalties to the objective functions. The penalty functions typically involve a tuning parameter that control the complexity of the selected model. The ability of the regularized variable selection methods to identify the true model critically depends on the correct choice of the tuning parameter. In this study we develop a consistent tuning parameter selection method for regularized Cox's proportional hazards model with a diverging number of parameters. The tuning parameter is selected by minimizing the generalized information criterion. We prove that, for any penalty that possesses the oracle property, the proposed tuning parameter selection method identifies the true model with probability approaching one as sample size increases. Its finite sample performance is evaluated by simulations. Its practical use is demonstrated in the Cancer Genome Atlas (TCGA) breast cancer data.

Keywords: Cox proportional hazards model; TCGA data; diverging number of parameter; generalized information criterion; tuning parameter selection; variable selection.