Analysis of incomplete data in quantile regression and semiparametric models

North Carolina State University, Raleigh NC

Investigators

Abstract

The principal investigator (PI) aims to develop new statistical methodology for analyzing incomplete data using regression of quantiles where causes of incomplete data are due to either censoring or measurement error. The research is challenging mainly because quantile regression aims to avoid parametric error distributional assumptions so the standard likelihood-based methods cannot be used. The PI will focus on three different but related problems. First, new approaches to estimation based on corrected scores will be developed to account for a class of measurement errors in the covariates. Second, an index-based estimation method will be proposed for censored quantile regression to accommodate high dimensional covariates. Penalization methods will be developed for variable selection. The third problem focuses on data with covariates subject to fixed censoring. To improve the efficiency over estimators from complete samples, a new multiple imputation approach based on censored regression of quantiles will be developed. The new imputation method can be used to improve statistical inference for not only quantile regression but also more general regression problems. The proposed research will have broad and valuable applicability in various fields, for instance, in microarray studies where the gene expression data are often measured with errors, in survival studies where random censoring is common, and in environmental and geological studies where measurements are often subject to fixed censoring. For example, in contrast to conventional statistical methods, quantile regression models can help discover heterogeneous effects of drug treatments on survival times of both high and low risk patients. The project will integrate research and education by developing advanced topics courses, mentoring students especially those from under-represented groups.