Empirical Likelihood and Censored Quantile Regression

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

This project is concerned with the development of statistical methodologies in the regression analysis of censored data that can model both the average and extreme responses. The investigators will develop a novel empirical likelihood (EL) approach for the accelerated failure time (AFT) model and censored quantile regression. Empirical likelihood is a recently developed nonparametric inference method with asymptotic properties similar to the parametric maximum likelihood. The novel EL approach uses sample points casewise and is less stringent than previously proposed residual based empirical likelihood: the sample points are not required to be identically distributed, and a more general form of heteroscedasticity is permitted. An interesting application of the proposed approach is to censored quantile regression. While quantile regression has appeared as an alternative to the least squares with uncensored data as it provides more complete information about the conditional distribution of the response, its application to censored data has been limited due to the lack of an efficient inference method, among other reasons. The proposed EL approach will advance quantile analysis in censored regression and extend the domain of EL inference in general. The proposed research is of high federal strategic interest because the results will accelerate many health, medical, and economic research projects where data is incomplete and abnormal cases rather than the average are of interest, such as low birth weight, high ozone concentration, cancer survival rates, or high yield stock, among others. Traditional analyses focus on the center of the data and implicitly assume that the results found for the average group are generalizable to the entire patient group. However, this is usually not the case. For example, an investigator in a survival study of cancer patients may find that certain molecular biomarkers are prognostic factors only for those ovarian cancer patients who die exceptionally early compared to others in the same reference group. The quantile regression technique with the proposed inference procedure permits the investigation of the biomarkers without constraining their effects for different subpopulations to be same as for the average group. Therefore, the proposed method can better inform health professionals of the effects of physiological and molecular biomarkers on different subpopulations and provide a useful prognostic tool for the overall and progression free survival times.