Date of Award

Fall 12-5-2011

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Gengsheng Qin


In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased and non-diseased groups, finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. This dissertation concentrates on statistical inferences for the Youden index. First, an auxiliary tool for the Youden index, called the diagnostic curve, is defined and used to evaluate the diagnostic test. Second, in the paired-design study to assess the diagnostic accuracy of two biomarkers, the difference in paired Youden indices frequently acts as an evaluation standard. We propose an exact confidence interval for the difference in paired Youden indices based on generalized pivotal quantities. A maximum likelihood estimate-based interval and a bootstrap-based interval are also included in the study. Third, for certain diseases, an intermediate level exists between diseased and non-diseased status. With such concern, we define the Youden index for three ordinal groups, propose the empirical estimate of the Youden index, study the asymptotic properties of the empirical Youden index estimate, and construct parametric and nonparametric confidence intervals for the Youden index. Finally, since covariates often affect the accuracy of a diagnostic test, therefore, we propose estimates for the Youden index with a covariate adjustment under heteroscedastic regression models for the test results. Asymptotic properties of the covariate-adjusted Youden index estimators are investigated under normal error and non-normal error assumptions.

Included in

Mathematics Commons