Polychotomization of continuous variables in regression models based on the overall C index

Area of Science:

• Biostatistics
• Medical Informatics
• Regression Analysis

Background:

• Continuous variables in regression models can be categorized for prediction tables.
• Existing methods for dichotomizing prognostic variables are limited.
• A need exists for integrated polychotomization methods, especially when dichotomization causes information loss or when central values represent normal states.

Purpose of the Study:

• To develop a theoretical and practical method for polychotomization of continuous independent variables.
• To address the limitations of existing dichotomization techniques.

Main Methods:

• Utilized the overall discrimination index C (Harrell's C) to measure predictive ability.
• Derived a mathematical method for polychotomization.
• Developed a parametric method to minimize positive bias observed in naive application.
• Assessed performance using Monte Carlo simulation.

Main Results:

• The overall C is strongly correlated with the area under the ROC curve.
• The polychotomized variable's predictive performance is comparable to the original continuous variable.
• The parametric method demonstrated minimal bias in performance estimates and cutoff points.
• Application to rhabdomyolysis data yielded probability profile tables for patient diagnosis/prognosis.

Conclusions:

• A novel polychotomization (including dichotomization) method for continuous variables in regression models was developed, based on the discrimination index C.
• A parametric approach effectively mitigates positive bias.
• The proposed method performs well and facilitates the creation of probability profile tables for clinical applications.