A smooth nonparametric approach to determining cut-points of a continuous scale

The problem of determining cut-points of a continuous scale according to an established categorical scale is often encountered in practice for the purposes such as making diagnosis or treatment recommendation, determining study eligibility, or facilitating interpretations. A general analytic framework was recently proposed for assessing optimal cut-points defined based on some pre-specified criteria. However, the implementation of the existing nonparametric estimators under this framework and the associated inferences can be computationally intensive when more than a few cut-points need to be determined. To address this important issue, a smoothing-based modification of the current method is proposed and is found to substantially improve the computational speed as well as the asymptotic convergence rate. Moreover, a plug-in type variance estimation procedure is developed to further facilitate the computation. Extensive simulation studies confirm the theoretical results and demonstrate the computational benefits of the proposed method. The practical utility of the new approach is illustrated by an application to a mental health study.