A general approach to categorizing a continuous scale according to an ordinal outcome

• We now discuss and evaluate alternative bootstrap inference procedures, as suggested by the Associate Editor and one referee.
• We now present regularity conditions in the main text and provide detailed discussions about these assumptions.
• We now make the theorem proofs clearer.
• We now fixed typos and incomplete references.
• In the response letter, we also clarify questions about the significance of this work.

In practice, disease outcomes are often measured in a continuous scale, and classification of subjects into meaningful disease categories is of substantive interest. To address this problem, we propose a general analytic framework for determining cut-points of the continuous scale. We develop a unified approach to assessing optimal cut-points based on various criteria, including common agreement and association measures. We study the nonparametric estimation of optimal cut-points. Our investigation reveals that the proposed estimator, though it has been ad-hocly used in practice, pertains to nonstandard asymptotic theory and warrants modifications to traditional inferential procedures. The techniques developed in this work are generally adaptable to study other estimators that are maximizers of nonsmooth objective functions while not belonging to the paradigm of M-estimation. We conduct extensive simulations to evaluate the proposed method and confirm the derived theoretical results. The new method is illustrated by an application to a mental health study.