Confidence interval estimation of the Youden index and corresponding cut-point for a combination of biomarkers under normality

In prognostic/diagnostic medical research, it is often the goal to identify a biomarker that differentiates between patients with and without a condition, or patients that will have good or poor response to a given treatment. The statistical literature is abundant with methods for evaluating single biomarkers for these purposes. However, in practice, a single biomarker rarely captures all aspects of a disease process; therefore, it is often the case that using a combination of biomarkers will improve discriminatory ability. A variety of methods have been developed for combining biomarkers based on the maximization of some global measure or cost-function. These methods usually create a score based on a linear combination of the biomarkers, upon which the standard single biomarker methodologies (such as the Youden's index) are applied. However, these single biomarker methodologies do not account for the multivariable nature of the combined biomarker score. In this article we present generalized inference and bootstrap approaches to estimating confidence intervals for the Youden's index and corresponding cut-point for a combined biomarker. These methods account for inherent dependencies and provide accurate and efficient estimates. A simulation study and real-world example utilize data from a Duchene Muscular Dystrophy study are also presented.