Sensitivity of health-related scales is a non-decreasing function of their classes

TL;DR

This paper proves that increasing the number of classes in health-related scales improves their sensitivity, offering a mathematical basis for designing more accurate diagnostic tools in clinical research.

Contribution

It provides a mathematical proof that the sensitivity of discrete health scales is non-decreasing with the number of classes, enhancing disease diagnosis methodologies.

Findings

Sensitivity is a non-decreasing function of the number of classes.

More classes lead to better classification accuracy.

Methodology for developing more precise diagnostic scales.

Abstract

In biomedical research the use of discrete scales which describe characteristics of individuals are widely applied for the evaluation of clinical conditions. However, the number of classes (partitions) used in a discrete scale has never been mathematically evaluated against the accuracy of a scale to predict the true cases. This work, using as accuracy markers the sensitivity and specificity, revealed that the number of classes of a discrete scale affects its estimating ability of correctly classifying the true diseased. In particular, it was proved that the sensitivity of scales is a non-decreasing function of the number of their classes. This result has particular interest in clinical research providing a methodology for developing more accurate tools for disease diagnosis.