Abstract:

This talk consists of two parts. 
In Part I, the two-sample semiparametric model will be reviewed. The empirical likelihood method is used to find the maximum likelihood estimates of the parameters and the underlying distribution functions. The relationship with the logistic regression will also be discussed. The test of goodness-of-fit of the model will be presented. Some generalizations and applications of the model are also to be reviewed.

In Part II, a recent application of the model to receiver operating characteristic (ROC) curve is to be presented. In 
medical diagnostic testing problems and other area, the covariate adjusted ROC curves have been discussed recently for achieving the best separation between disease and control. Due to various restrictions such as cost, the availability of patients, and ethic issue   quite frequently that only limited information is available. As a result, it is less likely  to have large enough overall sample size to support reliable direct estimations of ROCs for all the underlying covariates of interest. For example, some genetic factors are less commonly observable compared with others. To get an accurate covariate adjusted ROC estimation, novel statistical methods are needed to effectively utilize the limited information. Therefore, it is desirable to use indirect estimates that borrow strength by employing values of the variables of interest from neighboring covariates.In this paper we discuss two semiparametric exponential tilting models, where the density functions from different 
covariate levels share a common baseline density and the parameters in the exponential tilting component reflect the difference among covarities.With the proposed models, the estimated covariate adjusted ROC is much smoother and more efficient than the nonparametric counterpart without borrowing information from neighboring covariates.A simulation study and a real data application are reported.