Further Studies on Weighted Empirical Likelihood

The University Of Central Florida Board Of Trustees, Orlando FL

Investigators

Abstract

ABSTRACT: Since Owen (1988), the empirical likelihood method has been developed to construct tests and confidence sets based on nonparametric likelihood ratio. Studies have shown that the empirical likelihood ratio inferences are of comparable accuracy to alternative methods. However, so far the applications of empirical likelihood method to censored data are relatively few and are mainly focused on the right censored data. In this context, the PI discovered in her 2001-paper that a new likelihood function, called weighted empirical likelihood function, has the potential to facilitate the research on a broad class of nonparametric and semiparametric statistics for various types of incomplete data, including doubly censored data, interval censored data, and partly interval-censored data. It is shown that weighted empirical likelihood may be viewed as the asymptotic version of Owen's empirical likelihood function for censored data. In the past few years, the PI's investigation shows that the weighted empirical likelihood indeed provides a useful tool to deal with statistical inference problems with complicated types of censored data which are otherwise quite difficult to handle. The objective of this current project is to further study the applications of weighted empirical likelihood in providing solutions for several important nonparametric or semiparametric statistical inference problems in survival analysis with various types of censored data. The issues under consideration include: (1) extension of the weighted empirical likelihood to deal with p-dimensional variables; (2) further applications of the weighted empirical likelihood to estimation or model assessment problems associated with estimating equations, profile likelihood and some important survival models; (3) coverage accuracy of weighted empirical likelihood ratio confidence intervals; (4) comparison with alternative methods. Incomplete data are frequently encountered in medical follow-up and reliability studies. Recently, statisticians are paying more attention to some more complicated types of incomplete data, such as doubly censored data, interval censored data, partly interval-censored data, truncated data, etc., as these data occur in important clinical trials and scientific research. For instance, doubly censored data were encountered in a recent study of primary breast cancer, interval censored data were encountered in AIDS research, partly interval-censored data were encountered in heart disease and diabetes studies, and doubly truncated data were encountered in astronomical research. Up to now, the statistical research on these more complicated types of incomplete data still generally lags behind that on right censored data,mainly because it is technically much more challenging. The expected results of this project are better understanding of the technique of weighted empirical likelihood, and providing solutions for several important statistical inference problems associated with some widely used survival models in biomedical research and epidemiological studies when observed data are right censored, doubly censored, interval censored, or partly interval-censored.