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

Area of Science:

• Biostatistics
• Medical Informatics
• Epidemiology

Background:

• Disease outcomes are frequently measured on continuous scales, necessitating accurate classification into discrete categories.
• Establishing meaningful disease categories from continuous data is crucial for clinical practice and research.
• Existing methods for determining classification cut-points may lack a unified theoretical foundation.

Purpose of the Study:

• To propose a general analytic framework for determining optimal cut-points on continuous scales.
• To develop a unified approach for assessing optimal cut-points using various criteria.
• To investigate the nonparametric estimation of these optimal cut-points.

Main Methods:

• Developed a unified analytic framework for optimal cut-point determination.
• Employed nonparametric estimation techniques for cut-point assessment.
• Investigated the asymptotic theory and inferential procedures for the proposed estimator.

Main Results:

• The proposed nonparametric estimator, while used ad-hoc, requires modifications to traditional inferential procedures due to nonstandard asymptotic theory.
• The developed techniques are adaptable for other estimators maximizing nonsmooth objective functions outside M-estimation.
• Extensive simulations confirmed the theoretical results and evaluated the proposed method's performance.

Conclusions:

• The proposed framework offers a robust method for classifying subjects into meaningful disease categories from continuous data.
• The study highlights the need for modified inferential procedures for the proposed nonparametric estimator.
• The methodology is broadly applicable to statistical problems involving nonsmooth objective functions and classification.