Lease Square Kernel Machines for Semiparametric Regression in Microarray Pathway Analysis and Their

Speaker: Professor Xihong Lin
Department of Biostatistics
School of Public Health
University of Michigan

Time:1:00p.m. Monday 31st January 200
Venue: Red Center Room RC-4082
near Barker Street Gate 14

We consider a semiparametric regression model for modelling modeling the effects of covariates and microarray pathways on health outcomes. This model relates a normal outcome to covariates and gene expressions, where the covariate effects are modelled parametrically and gene expression effects are modelled 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 the genes are likely to interact with each other in a complicated way.

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 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. A bootstrap test is developed to test for significant gene expression effects. The methods are illustrated using a prostate cancer data set and evaluated using simulations.

Y. Fan
E-mail yanan@maths.unsw.edu.au