The Effect of Verification Bias in the Naïve Estimators of Accuracy of a Binary Diagnostic Test

Abstract

The assessment of a binary diagnostic test requires a knowledge of the disease status of all the patients in the sample through the application of a gold standard. In practice, the gold standard is not always applied to all of the patients, which leads to the problem of partial verification of the disease. When the accuracy of the diagnostic test is assessed using only those patients whose disease status has been verified using the gold standard, the estimators obtained in this way, known as Naïve estimators, may be biased. In this study, we obtain the explicit expressions of the bias of the Naïve estimators of sensitivity and specificity of a binary diagnostic test. We also carry out simulation experiments in order to study the effect of the verification probabilities on the Naïve estimators of sensitivity and specificity.

Keywords:

• Naïve estimator
• Partial verification
• Sensitivity
• Specificity
• Verification bias

Mathematics Subject Classification:

• 92B15
• 62P10

Acknowledgment

This research was supported by the Spanish Ministry of Science and Technology. Grant number BFM2003-08950. We thank the editor and referees of Communications in Statistics.

Notes

Between parentheses are shown the probabilities of the multinomial distribution.

MSE: Mean squared error. SE: Standard error.

SE: Standard error.

MSE: Mean squared error. SE: Standard error.

SE: Standard error.