This article studies the problem of combining correlated diagnostic tests to maximize the discriminating power between the diseased population and the healthy population. The authors consider all possible linear combinations of multiple diagnostic tests and search for the one that achieves the largest area under the receiver operating characteristic (ROC) curve. They discuss the statistical estimation of the optimum linear combination test and the associated maximum area under the ROC curve. Their approach is based on the assumption of multivariate normal distribution of the multiple diagnostic tests. They also present the application of the proposed techniques to the neuropathologic diagnosis of Alzheimer's disease based on brain lesions from 5 different brain locations using a data set from the Washington University Alzheimer's Disease Research Center.
- Confidence interval estimate
- Maximum likelihood estimate
- Receiver operating characteristic (ROC) curve
- Z transformation