Semiparametric Regression for High-dimensional Data with Applications in Microarrays: Least Square Kernel Machines and Linear Mixed Models

• Activity Number: 296
• Type: Invited
• Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Committee on Women in Statistics
• Author(s): Xihong Lin*+ and Dawei Liu and Debashis Ghosh
• Companies: Harvard University and University of Michigan and University of Michigan
• Keywords: gene expression ; nonparametric regression ; dual problem ; primal problem ; penalized likelihod ; BLUPs

Abstract

In this paper, we consider a semiparametric regression model for modeling high-dimensional covariate data (e.g., microarrays). This model relates a normal clinical outcome to clinical covariates and gene expressions, where the clinical covariate effects are modeled parametrically and gene expression effects are modeled nonparametrically using least square kernel machines (LSKMs). The nonparametric function of gene expressions allows for the possibility that the number of genes might be large and that the genes are likely to interact. We show that the dual problem derived from the primal problem of the least square kernel machine 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 least square kernel machine estimator of the nonparametric gene expression function can be obtained using the Best Linear Unbiased Predictor in linear mixed models. The smoothing parameter and the kernel scale parameter can be estimated as variance components using REML in linear mixed models.