Verification bias-corrected estimators of the relative true and false positive rates of two binary screening tests

The relative accuracy of two binary screening tests can be quantified by estimating the relative true positive rate (rTPR) and relative false positive rate (rFPR) between the two tests. Ideally all study subjects are administered both screening tests as well as a gold standard to determine disease status. In practice, however, often the gold standard is so invasive or costly that only a percentage of study subjects receive disease verification and the percentage differs depending on the results of the two screening tests. This is known as verification-biased sampling and may be by design or due to differential patient dropout or refusal to have the gold standard test administered. In this paper, maximum likelihood estimators of rTPR and rFPR and corresponding confidence intervals are developed for studies with verification-biased sampling assuming that disease status is missing at random (MAR). Simulation studies are used to show that if the MAR assumption holds, then the verification bias-corrected point estimators have little small sample bias and the confidence intervals have good coverage probabilities. Simulation studies also demonstrate that the verification bias-corrected point estimators may not be robust to violation of the MAR assumption. The proposed methods are illustrated using data from a study comparing the accuracy of Papanicolaou and human papillomavirus tests for detecting cervical cancer.