Abstract: The receiver operating characteristic (ROC) curve provides a comprehensive performance assessment of a continuous biomarker over the full threshold spectrum. Nevertheless, a medical test often dictates operating at a certain high level of sensitivity or specificity. A diagnostic accuracy metric directly targeting clinical utility is specificity at the controlled sensitivity level, or vice versa. While the empirical point estimation is readily adopted in practice, the nonparametric interval estimation is difficult because the variance involves density functions, owing to the estimated threshold. In addition, even with a fixed threshold, many standard confidence intervals for the binomial proportion, including the Wald interval, can exhibit erratic behaviors. This study is motivated by the superior performance of the score interval for binomial proportion, and we propose a novel extension for the biomarker problem. We also develop an exact bootstrap procedure and establish the consistency of the bootstrap variance estimator. Both single-biomarker evaluation and two-biomarker comparison are investigated. Extensive simulation studies demonstrated competitive performance of our proposals. An application to aggressive prostate cancer diagnosis is also provided.

Key words and phrases: Diagnostic test, exact bootstrap, score confidence interval, sensitivity at controlled specificity, specificity at controlled sensitivity.