Joint comparison of the predictive values of multiple binary diagnostic tests: an extension of McNemar’s test

ABSTRACT

Positive and negative predictive values are important measures of the clinical accuracy of a diagnostic test. Various test statistics have been proposed to compare positive predictive values or negative predictive values of two binary diagnostic tests separately. However, such separate comparisons do not present a complete picture of the relative accuracy of the two diagnostic tests. In this paper, we propose an extension of McNemar’s test for the joint comparison of predictive values of multiple diagnostic tests. The proposed extended McNemar’s test is intuitive and simple to compute, only involving cell counts of discordant pairs from multiple $2\times 2$ tables. Furthermore, we also propose a re-formulation of an existing Wald test statistic so that it can be implemented more easily than its original form. Simulations demonstrate that the proposed extended McNemar’s test statistic preserves type one error much better than the existing Wald test statistic. Thus, we believe that the proposed extended McNemar’s test statistic is the preferred statistic to simultaneously compare the predictive values of multiple binary diagnostic tests.

KEYWORDS:

• Predictive values
• sensitivity and specificity
• multiple binary diagnostic tests
• McNemar’s test
• joint comparison
• global test
• extended McNemar’s test

Acknowledgments

I would like to thank the editor, the associate editor, and two anonymous referees for their valuable comments that resulted in an improved version of this paper.

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No potential conflict of interest was reported by the author(s).

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Funding

The author(s) reported there is no funding associated with the work featured in this article.