Sample size calculation for comparing two ROC curves

Biomarkers are key components of personalized medicine. In this paper, we consider biomarkers taking continuous values that are associated with disease status, called case and control. The performance of such a biomarker is evaluated by the area under the curve (AUC) of its receiver operating characteristic curve. Oftentimes, two biomarkers are collected from each subject to test if one has a larger AUC than the other. We propose a simple non-parametric statistical test for comparing the performance of two biomarkers. We also present a simple sample size calculation method for this test statistic. Our sample size formula requires specification of AUC values (or the standardized effect size of each biomarker between cases and controls together with the correlation coefficient between two biomarkers), prevalence of cases in the study population, type I error rate, and power. Through simulations, we show that the testing on two biomarkers controls type I error rate accurately and the proposed sample size closely maintains specified statistical power.