Exact inference for the Youden index to discriminate individuals using two-parameter exponentially distributed pooled samples

It has become increasingly common in epidemiological studies to pool specimens across subjects as a useful cot-cutting technique to achieve accurate quantification of biomarkers and certain environmental chemicals. The data collected from these pooled samples can then be utilized to estimate the Youden Index, which measures biomarker's effectiveness and aids in the selection of an optimal threshold value, as a summary measure of the Receiver Operating Characteristic curve. The aim of this paper is to make use of generalized approach to estimate and testing of the Youden index. This goal is accomplished by the comparison of classical and generalized procedures for the Youden Index with the aid of pooled samples from the shifted-exponentially distributed biomarkers for the low-risk and high-risk patients. These are juxtaposed using confidence intervals, p-values, power of the test, size of the test, and coverage probability with a wide-ranging simulation study featuring a selection of various scenarios. In order to demonstrate the advantages of the proposed generalized procedures over its classical counterpart, an illustrative example is discussed using the Duchenne Muscular Dystrophy data available at http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets or http://lib.stat.cmu.edu/datasets/.