Effect of verification bias on positive and negative predictive values

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Abstract
The pairing of sensitivity and specificity expresses the efficacy of a test, and positive and negative predictive values measure the accuracy of a diagnostic test when applied to a particular patient. To calculate these measures, one has to know the true disease status of each patient. In practice, however, some patients may not be selected for verification of disease status. It has been shown that the estimated sensitivity and specificity may be biased if one includes in the study sample only the patients with verified disease statuses. This paper concerns the properties of the estimators of positive and negative predictive values using only patients with verified disease statuses. First, I show that these estimators are unbiased and provide consistent estimators for the variances of these estimators under the assumption that the probability of selecting a patient for a disease verification procedure does not depend directly on the true disease status of the patient. Then, I use the ML method to study the sensitivity of the naive estimators to the departure from the conditional independence assumption.

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