Interval estimation for operating characteristic of continuous biomarkers with controlled sensitivity or specificity

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 to operate at a certain high level of sensitivity or specificity. A diagnostic accuracy metric directly targeting the 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 challenged by the fact that the variance involves density functions due to estimated threshold. In addition, even with a fixed threshold, many standard confidence intervals including the Wald interval for binomial proportion could have erratic behaviors. In this article, we are motivated by the superior performance of the score interval for binomial proportion and propose a novel extension for the biomarker problem. Meanwhile, we develop exact bootstrap and establish consistency of the bootstrap variance estimator. Both single-biomarker evaluation and two-biomarker comparison are investigated. Extensive simulation studies were conducted, demonstrating competitive performance of our proposals. An illustration with aggressive prostate cancer diagnosis is provided.