ROC Curve Analysis for Randomly Selected Patients

Abstract

Receiver operating characteristic (ROC) curves and the area under the curve (AUC) are widely used in medical studies to examine the effectiveness of markers in diagnosing diseases. In most of the existing literature for ROC curve analysis it is assumed that the healthy and the diseased populations are independent of each other, which may lead to bias in the studies. In this paper we consider the disease status as a binary random variable. Assuming the disease status is determined by a latent variable and the marker and the latent variable have a bivariate normal distribution, we derive the properties of the ROC curve and the AUC. We also look at the problem of choosing optimum combination of markers when multiple markers are present. Limiting distributions are obtained and confidence intervals are discussed as well. A small simulation study is performed which confirms the superiority of our methods over the general practice of considering the two populations to be independent.