Semi-Empirical Likelihood Confidence Intervals for the ROC Curve with Missing Data

The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performances of two or more laboratory or diagnostic tests. In this thesis, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric while the other one is non-parametric and both populations have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It has been shown that the log-semi-empirical likelihood ratio statistic is asymptotically chi-square distributed. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. Simulation studies are conducted to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing rates. INDEX WORDS: Confidence interval, Empirical likelihood, Estimating equation, Missing data, ROC curve SEMI-EMPIRICAL LIKELIHOOD CONFIDENCE INTERVALS FOR THE ROC CURVE WITH MISSING DATA