Nonparametric predictive inference for comparison of two diagnostic tests

Abstract

An important aim in diagnostic medical research is comparison of the accuracy of two diagnostic tests. In this paper, comparison of two diagnostic tests is presented using nonparametric predictive inference (NPI) for future order statistics. The tests are assumed to be applied on the same individuals from two groups, e.g., healthy and diseased individuals, or from three groups with a known ordering, e.g., adding a group of severely diseased individuals to the two group scenario. Our comparison is explicitly in terms of lower and upper probabilities for proportions of correctly diagnosed future individuals from each group, for a given total number of such individuals. We include in our comparison the possibility that it is more important to get a correct diagnosis for individuals from one group than from another group.

Keywords:

• Comparing two diagnostic tests
• lower and upper probabilities
• nonparametric predictive inference

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G86
• 62P10
• 62P99
• 62G99
• 60A99

Acknowledgments

We are grateful to Prof. Sarafidis for providing the data set used in Example 4.1. The authors are grateful to the anonymous reviewer whose supportive comments led to improved presentation of the paper.