Gold standards are out and Bayes is in: Implementing the cure for imperfect reference tests in diagnostic accuracy studies

Bayesian mixture models, often termed latent class models, allow users to estimate the diagnostic accuracy of tests and true prevalence in one or more populations when the positive and/or negative reference standards are imperfect. Moreover, they allow the data analyst to show the superiority of a novel test over an old test, even if this old test is the (imperfect) reference standard. We use published data on Toxoplasmosis in pigs to explore the effects of numbers of tests, numbers of populations, and dependence structure among tests to ensure model (local) identifiability. We discuss and make recommendations about use of priors, sensitivity analysis, model identifiability and study design options, and strongly argue for the use of Bayesian mixture models as a logical and coherent approach for estimating the diagnostic accuracy of two or more tests.