Estimating the Area under a Receiver Operating Characteristic Curve For Repeated Measures Design

The receiver operating characteristic (ROC) curve is widely used for diagnosing as well as for judging the discrimination ability of different statistical models. Although theories about ROC curves have been established and computation methods and computer software are available for cross-sectional design, limited research for estimating ROC curves and their summary statistics has been done for repeated measure designs, which are useful in many applications, such as biological, medical and health services research. Furthermore, there is no published statistical software available that can generate ROC curves and calculate summary statistics of the area under a ROC curve for data from a repeated measures design. Using generalized linear mixed model (GLMM), we estimate the predicted probabilities of the positivity of a disease or condition, and the estimated probability is then used as a bio-marker for constructing the ROC curve and computing the area under the curve. The area under a ROC curve is calculated using the Wilcoxon non-parametric approach by comparing the predicted probability of all discordant pairs of observations. The ROC curve is constructed by plotting a series of pairs of true positive rate (sensitivity) and false positive rate (1- specificity) calculated from varying cuts of positivity escalated by increments of 0.005 in predicted probability. The computation software is written in SAS/IML/MACRO v8 and can be executed in any computer that has a working SAS v8 system with SAS/IML/MACRO.