The sensitivity (Se) and the specificity (Sp) are the two most common measures of the performance of a diagnostic test, where Se is the probability of a diseased individual to be correctly identified by the test while Sp is the probability of a healthy individual to be correctly identified by the same test. A problem appears when all individuals cannot be verified by a gold standard. This occurs when there is not a definitive test for detection of the disease or the verification by a gold standard is an impracticable procedure according to its cost, accessibility or risks. In this paper we develop a Bayesian analysis to estimate the disease prevalence, the sensitivity and specificity of screening tests in the presence of a covariate and in the absence of a gold standard. We use the Metropolis–Hastings algorithm to obtain the posterior summaries of interest. We have as motivation for the investigation the LAMS (Latin American Screening) Study, an extensive project designed for comparing screening tools for cervical cancer in Brazil and Argentina. When applied to the analysis of data from LAMS Study, the proposed Bayesian method shows to be a useful alternative to estimate measures of performance of screening tests in the presence of covariates and when a gold standard is not available. An advantage of the method is the fact that the number of parameters to be estimated is not limited by the number of observations, as it happens with several frequentist approaches. However, it is important to point out that the Bayesian analysis requires informative priors in order for the parameters to be identifiable. The method can be easily extended for the analysis of other medical data sets.
"Bayesian estimation of performance measures of screening tests in the presence of covariates and absence of a gold standard." Braz. J. Probab. Stat. 23 (1) 68 - 81, June 2009. https://doi.org/10.1214/08-BJPS006