Relationships among sensitivity, specificity, and predictive values for a concave ROC curve
Abstract
.Evaluating medical tests relies on quantitative biomarkers, with sensitivity and specificity serving as two fundamental performance measures. In this article, we examine the interrelationships among sensitivity, specificity, and the test’s predictive values. Our analysis is based on the risk function – an increasing function representing the conditional probability of disease given the biomarker value. We show that sensitivity and specificity move in opposite directions. Similarly, the positive predictive value varies inversely with sensitivity, and the negative predictive value varies inversely with specificity.
Fields of Study & Subjects
Statistical Methods in Epidemiology
Probability and Statistical Research
Probabilistic Statistics in Medicine
Publication details
- Journal / source
- Communication in Statistics- Theory and Methods
- Volume
- 55
- Issue
- 14
- Pages
- 4540–4549
- Publication date
- 2 February 2026
- Language
- EN