Weighted Youden index and its two-independent-sample comparison based on weighted sensitivity and specificity

Most indices for evaluating a diagnostic test can be expressed as functions of sensitivity (SEN) and specificity (SPE). Practically, all existing methods suffer from the inability to weight sensitivity and specificity relative to their importance. In this paper, we developed a novel index, the weighted Youden index, that allows Youden index to be a combination of sensitivity and specificity with user-defined weights.

The weighted Youden index Jw is defined as Jw = 2(w×SEN + (1-w)SPE)-1 (0 ≤ w ≤ 1). It has three properties: (1) the sum of the weights which are attached to sensitivity and specificity should be equal to 1; (2) the range of Jw should be within [-1, 1], which is the range of the Youden index J; (3) Jw should be equal to J when sensitivity and specificity have equal weights. According to the central limit theorem, we obtain the standard error of Jw, and propose a statistical inference method to compare two weighted Youden indices. The monotonicity of the test statistic was discussed.

An example of comparing two diagnostic tests for pheochromocytoma was used to demonstrate the weighted Youden index method. Weighted Youden index, the confidence interval for each test and the hypothesis test of comparing two independent diagnostic tests were presented. Assigning the weights is essential to the weighted Youden index approach.

The weighted Youden index can broaden its applications in diagnostic test development and motivate further research in weighting sensitivity and specificity explicitly.