Semiparametric Logistic Regression for Classification of Gene Expression Microarrays: Support Vector Machines and Mixed Models

• Activity Number: 155
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Dawei Liu*+ and Xihong Lin and Debashis Ghosh
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: semiparametric ; logistic regression ; support vector machine ; mixed model

Abstract

In disease diagnosis, classification of patient samples plays a much important role. For some diseases both clinical covariates and gene expressions should be considered simultaneously in making decisions on disease status. We propose a semiparametric logistic regression model to relate a binary clinical outcome to clinical covariates and gene expressions, where the clinical covariate effects are modeled parametrically and gene expression effects are modeled nonparametrically using the support vector machine. The nonparametric function of gene expressions allows for the fact that the number of genes is likely to be large and the genes are likely to interact with each other. We show that the dual problem of the primal support vector machine problem can be formulated using a linear mixed effects model. Estimation hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the clinical covariate effects and the support vector estimator of the nonparametric gene expression function can be obtained using the Best Linear Unbiased Predictor in linear mixed models.