NEW METHODS FOR VARIABLE SELECTION WITH APPLICATIONS TO SURVIVAL ANALYSIS AND STATISTICAL REDUNDANCY ANALYSIS USING GENE EXPRESSION DATA by

by Simin Hu An important application of microarray research is to develop cancer diagnostic and prognostic tools based on tumor genetic profiles. For easy interpretation, such studies aim to identify a small fraction of genes to build molecular predictors of clinical outcomes from at least thousands of genes thus require methodologies that can model high dimensional covariates and accomplish variable selection simultaneously. One interesting area is modeling cancer patients’ survival time or time to cancer reoccurrence with gene expression data. In the first part of this dissertation, we propose a new penalized weighted least squares method for model estimation and variable selection in accelerated failure time models. In this method, right censored observations are used as censoring constraints in optimizing the weighted least squares objective function. We also include ridge penalty to deal with singularity caused by collinearity and high dimensionality and use the least absolute shrinkage and selection operator to achieve