Abstract
The receiver operating characteristic (ROC) curve can be utilized to evaluate the performance of diagnostic tests. The area under the ROC curve (AUC) is a widely used summary index for comparing multiple ROC curves. Both parametric and nonparametric methods have been developed to estimate and compare the AUCs. However, these methods are usually only applicable to data collected from simple random samples and not surveys and epidemiologic studies that use complex sample designs such as stratified and/or multistage cluster sampling with sample weighting. Such complex samples can inflate variances from intra-cluster correlation and alter the expectations of test statistics because of the use of sample weights that account for differential sampling rates. In this paper, we modify the nonparametric method to incorporate sampling weights to estimate the AUC and employ leaving-one-out jackknife methods along with the balanced repeated replication method to account for the effects of the complex sampling in the variance estimation of our proposed estimators of the AUC. The finite sample properties of our methods are evaluated using simulations, and our methods are illustrated by comparing the estimated AUC for predicting overweight/obesity using different measures of body weight and adiposity among sampled children and adults in the US Hispanic Health and Nutrition Examination Survey.