Prevalence estimation when disease status is verified only among test positives: Applications in HIV screening programs.

The first goal of the United Nations' 90-90-90 HIV/AIDS elimination strategy is to ensure that, by 2020, 90% of HIV-positive people know their HIV status. Estimating the prevalence of HIV among people eligible for screening allows assessment of the number of additional cases that might be diagnosed through continued screening efforts in this group. Here, we present methods for estimating prevalence when HIV status is verified by a gold standard only among those who test positive on an initial, imperfect screening test with known sensitivity and specificity. We develop maximum likelihood estimators and asymptotic confidence intervals for use in 2 scenarios: when the total number of test negatives is known (Scenario 1) and unknown (Scenario 2). We derive Bayesian prevalence estimators to account for non-negligible uncertainty in previous estimates of the sensitivity and specificity. The Scenario 1 estimator consistently outperformed the Scenario 2 estimator in simulations, demonstrating the use of recording the number of test negatives in public health screening programs. For less accurate tests (sensitivity and specificity < 90%), the performance of the 2 estimators was comparable, suggesting that, under these circumstances, prevalence can still be estimated with adequate precision when the number of test negatives is unknown. However, use of the Bayesian approach to account for uncertainty in the sensitivity and specificity is especially recommended for the Scenario 2 estimator, which was particularly sensitive to misspecification of these values. R code for implementing these methods is available at hsph.harvard.edu/donna-spiegelman/software.