BAYESIAN analysis of the performance of two diagnostic tests when negative individuals on both tests are not verified by a gold standard

Edson Zangiacomi Martinez[1]

Jorge Alberto Achcar[2]

Francisco Louzada-Neto2

§       ABSTRACT: The performance of a diagnostic test is usually summarised by its sensitivity and specificity. Sensitivity is the probability of a positive result, given that the individual is truly diseased, and specificity is the probability of a negative result, given a nondiseased individual. These measures are obtained by comparing the test outcomes and the results of a reference test generically denominated gold standard. However, in many applied problems the gold standard is not available for those individuals with negative results on both tests. In this context, we develop a Bayesian inference procedure for performance measures estimation. We also present an extension of this procedure, involving inclusion of covariates. This Bayesian approach is based on Markov Chain Monte Carlo methods. As an example, we apply the proposed method to a real data set obtained from the medical literature.

§       KEYWORDS: Sensitivity; specificity; diagnostic tests; Bayesian methods.


[1]Departamento de Medicina Social, Faculdade de Medicina de Ribeirão Preto - FMRP, Universidade de São Paulo – USP, CEP 14049-900,  Ribeirão Preto, SP, Brasil. E-mail:

[2]Departamento de Estatística, Universidade Federal de São Carlos – UFSCar, Caixa Postal 676, CEP 13565-905,  São Carlos, SP, Brasil. E-mail: /