Confidence intervals for parameters of two diagnostic tests in the absence of a gold standard

We derive a profile-likelihood confidence interval and a score based confidence interval to estimate the population prevalences, test sensitivities, and test specificities of two conditionally independent diagnostic tests when no gold standard is available. We are motivated by a real-data example on the study of the properties for two fallible diagnostic tests for bovine immunodeficiency virus. We compare the coverage and average width of two new intervals with an interval based on the asymptotic normality of the maximum likelihood estimator and a Bayesian interval estimator via Monte Carlo simulation. We determine that for the parameter configurations considered here, the profile-likelihood, score, and Bayesian intervals all perform adequately in terms of coverage, but overall, the profile-likelihood interval performs best in terms of yielding at least nominal coverage with minimum expected width.