Structure Selection and Estimation for the Cox's Model in the Partially Linear Model Framework

• Activity Number: 296
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chen-Yen Lin*+ and Hao (Helen) Zhang
• Companies: Eli Lilly and Company and University of Arizona
• Keywords: LASSO ; COSSO ; partially linear model ; Cox's model

Abstract

We propose a novel regularization method for the Cox's proportional hazards model in the partially linear model framework. In the partially linear models, the choice of model structure, that is, deciding which predictors are linear and which are nonlinear, is crucial to improve the efficiency from parametric and nonparametric models. In practice, the specification depends on researcher's prior knowledge and pilot study to decide the model structure so that the applications of the partially linear models could be hindered. The proposed procedure automatically selects the structure of the partially linear model without prior specification and performs variable selection for the linear and nonlinear components simultaneously. This joint task can be achieved using a mixture of the adaptive LASSO and COSSO penalties. The proposed procedure improves the limitations of the existing methods and extends the applicability of the partially linear model to more exploratory analysis. We demonstrate the superior performance of the new procedure using simulations and real example.