Construction of confidence intervals for the maximum of the Youden index and the corresponding cutoff point of a continuous biomarker

Abstract

Evaluation of the overall accuracy of biomarkers might be based on average measures of the sensitivity for all possible specificities -and vice versa- or equivalently the area under the receiver operating characteristic (ROC) curve that is typically used in such settings. In practice clinicians are in need of a cutoff point to determine whether intervention is required after establishing the utility of a continuous biomarker. The Youden index can serve both purposes as an overall index of a biomarker's accuracy, that also corresponds to an optimal, in terms of maximizing the Youden index, cutoff point that in turn can be utilized for decision making. In this paper, we provide new methods for constructing confidence intervals for both the Youden index and its corresponding cutoff point. We explore approaches based on the delta approximation under the normality assumption, as well as power transformations to normality and nonparametric kernel- and spline-based approaches. We compare our methods to existing techniques through simulations in terms of coverage and width. We then apply the proposed methods to serum-based markers of a prospective observational study involving diagnosis of late-onset sepsis in neonates.

Keywords: Box-Cox transformation; ROC curve; Youden index; delta method; kernels; sensitivity; specificity; splines.