First, we propose a semiparametric statistic for comparing two correlated ROC curves under a marginal density ratio model. When comparing the accuracies of two diagnostic tests, a paired design is often used, in which both diagnostic tests are administered on the same patient. As a result, the two ROC curves are correlated. A joint model makes assumption on the correlation structure which might be too strong and hard to be verified, thus risks misspecification bias when the model assumption is not correctly specified. The proposed marginal density ratio model relaxes this assumption on the correlation structure and is more robust.
Second, we consider fitting logistic regression models to $2× 2$ contingency tables and derive explicit formulas for the maximum likelihood estimator, the asymptotic covariance matrix, the Wald statistic, the likelihood ratio statistic, and the score statistic in terms of the four cell frequency counts. We derive the asymptotic distributions of the Wald statistic, the likelihood ratio statistic, and the score statistic under local alternatives to the null hypothesis. We present some results on analysis of one real dataset.
Finally, we conduct a simulation study on comparison of various estimating methodologies under the situation when some covariate variables have missing values. Missing data analysis is among the most popular methodology in modern statistics. The existing methodologies apply mostly when the missing values occur in the response variable. We examine their performance when the missing values occur in the covariate variables.