Generalization of Youden index for multiple-class classification problems applied to the assessment of externally validated cognition in Parkinson disease screening

Routine cognitive screening in Parkinson disease (PD) has become essential for management, to track progression and to assess clinical status in therapeutic trials. Patients with mild cognitive impairment (PD-MCI) are more likely to progress to dementia and therefore need to be distinguished from patients with normal cognition and those with dementia. A three-class Youden index has been recently proposed to select cut-off points in three-class classification problems. In this article, we examine properties of a modification of the three-class Youden index and propose a generalization to k-class classification problems. Geometric and theoretical properties of the modified index Jk are examined. It is shown that Jk is equivalent to the sum of the k-1 two-class Youden indices for the adjacent classes of the ordered alternative problem given that the ordering holds. Methods are applied in the assessment of the Montreal Cognitive Assessment test when screening cognition in PD. © 2012 John Wiley & Sons, Ltd.