A Flexible Procedure to Analyze High-Dimensional Data with Discrete Responses

• Activity Number: 369
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xiang Liu* and Tian Chen and Yuanzhang Li and Hua Liang
• Companies: University of South Florida and University of Rochester and Walter Reed Army Institute of Research and The George Washington University
• Keywords: Generalized additive partially linear models ; LASSO ; Bootstrap ; Group selection ; Penalized quasi-likelihood

Abstract

Building a good model to explore the relationship between high-dimensional covariates and binary responses is not easy. One challenge comes from the large number of covariates especially when the number of covariates ($p$) is larger than the number of observations ($n$). Another challenge is that the assumption of a linear relationship between the covariates and log-odds-ratio in logistic regression (which is commonly used for binary response) may not fit the data well. In order to address the two challenges, we propose a procedure of building models to analyze high-dimensional data. Generalized additive partially linear models (GAPLM) are used to model the effects of covariates on the responses, which allow nonlinear effects of some covariates on the log-odds-ratio. The covariates in the model are determined by a novel variable selection method using bootstrapping and penalized regression. We apply the procedure to analyze data from a breast cancer study and an HIV study. The two examples show that the proposed procedure is very flexible and practically useful. A simulation study is also conducted to show the good performance of the procedure.