A Dunnett-Type Test and Its Sample Size Calculation for Comparing K ROC Curves with a Control

Abstract

Diagnostic biomarkers are key components of diagnostics. In this paper, we consider diagnostic biomarkers taking continuous values that are associated with a dichotomous disease status, called malignant or benign. The performance of such a biomarker is evaluated by the area under the curve (AUC) of its receiver operating characteristic curve. We assume that, together with the disease status, one control and multiple experimental biomarkers are collected from each subject to test if any of the experimental biomarkers have a larger AUC than the control. In this case, each experimental biomarker will be compared with the control so that a multiple testing issue is involved in the comparisons. In this paper, we propose a simple non-parametric statistical testing procedure to compare K(≥2) experimental biomarkers with a control, adjusting for the multiplicity and its sample size calculation method. Our sample size formula requires the specification of the AUC values (or the standardized effect size of each biomarker between the benign and malignant groups) together with the correlation coefficients between the biomarkers, the prevalence of the malignant group in the study population, the type I error rate, and the power. Through simulations, we show that the statistical test controls the overall type I error rate accurately and the proposed sample size closely maintains the specified statistical power.