The effect of verification bias on the comparison of predictive values of two binary diagnostic tests

Abstract

The comparison of the accuracy of two binary diagnostic tests has traditionally required knowledge of the disease status in all of the patients in the sample via the application of a gold standard. In practice, the gold standard is not always applied to all patients in a sample, and the problem of partial verification of the disease arises. The accuracy of a binary diagnostic test can be measured in terms of positive and negative predictive values, which represent the accuracy of a diagnostic test when it is applied to a cohort of patients. In this paper, we deduce the maximum likelihood estimators of predictive values (PVs) of two binary diagnostic tests, and the hypothesis tests to compare these measures when, in the presence of partial disease verification, the verification process only depends on the results of the two diagnostic tests. The effect of verification bias on the naïve estimators of PVs of two diagnostic tests is studied, and simulation experiments are performed in order to investigate the small sample behaviour of hypothesis tests. The hypothesis tests which we have deduced can be applied when all of the patients are verified with the gold standard. The results obtained have been applied to the diagnosis of coronary stenosis.