Estimating Disease Prevalence in a Bayesian Framework Using Probabilistic Constraints

Abstract

Studies sometimes estimate the prevalence of a disease from the results of one or more diagnostic tests that are applied to individuals of unknown disease status. This approach invariably means that, in the absence of a gold standard and without external constraints, more parameters must be estimated than the data permit. Two assumptions are regularly made in the literature, namely that the test characteristics (sensitivity and specificity) are constant over populations and the tests are conditionally independent given the true disease status. These assumptions have been criticized recently as being unrealistic. Nevertheless, to estimate the prevalence, some restrictions on the parameter estimates need to be imposed. We consider 2 types of restrictions: deterministic and probabilistic restrictions, the latter arising in a Bayesian framework when expert knowledge is available. Furthermore, we consider 2 possible parameterizations allowing incorporation of these restrictions. The first is an extension of the approach of Gardner et al and Dendukuri and Joseph to more than 2 diagnostic tests and assuming conditional dependence. We argue that this system of equations is difficult to combine with expert opinions. The second approach, based on conditional probabilities, looks more promising, and we develop this approach in a Bayesian context. To evaluate the combination of data with the (deterministic and probabilistic) constraints, we apply the recently developed Deviance Information Criterion and effective number of parameters estimated (pD) together with an appropriate Bayesian P value. We illustrate our approach using data collected in a study on the prevalence of porcine cysticercosis with verification from external data.

Post-mortem examination and laboratory-based analysis for the diagnosis of bovine tuberculosis among dairy cattle in Ecuador

“…The true prevalence (TP) based on detection of gross visible lesions was calculated using the RoganGladen's Equation (1978) under a Bayesian modelling approaches (Berkvens et al, 2006). The Rogan-Gladen equation describes the estimation of TP through the apparent prevalence (P ), and the Se, and Sp of a test…”

“…Since there is no gold standard test, TP must be estimated imposing constraints on the parameters (Berkvens et al, 2006). Bayesian approach lets to incorporate external information by specifying prior distributions on the parameters, i.e., prior knowledge and/or beliefs regarding to Se and Sp of necropsy (Enoe et al, 2000;Branscum et al, 2005).…”

Bayesian estimation of true prevalence, sensitivity and specificity of indirect ELISA, Rose Bengal Test and Slow Agglutination Test for the diagnosis of brucellosis in sheep and goats in Bangladesh

“…A Bayesian latent class analysis was implemented in WinBUGS 1.4 (Spiegelhalter et al, 2003) and R 2.14.2 (R Foundation and Statistical Computing 2012) to estimate the prevalence, sensitivity and specificity of the three tests, using models developed by Branscum et al (2005), Berkvens et al (2006), Nérette et al (2008) and Haley et al (2011) separately for sheep and goats. In a three test scenario, 7 parameters need to be estimated by the multinominal model under the assumption of conditional independence namely; the prevalence, and the sensitivities and specificities of the three tests.…”

“…As none of the three tests is considered a gold standard test and the tests are not conditionally independent, constraints have to be imposed on a subset of the parameters in order to make the models identifiable (Branscum et al, 2005). To evaluate the goodness of fit of the models, the posterior predictive p-value, Deviance Information Criterion (DIC) (Spiegelhalter et al, 2002) and the number of effectively estimated parameters (pD) (Berkvens et al, 2006) were used as calibrating parameters. Briefly, the DIC ensures that a parsimonious model is selected.…”

“…However, the gold standard for the diagnosis of brucellosis is isolation and identification of the organism (Alton et al, 1988;OIE, 2008) which is not easy to perform in a developing and resource-limited country like Bangladesh. In the absence of a gold standard, simultaneous estimation of true prevalence and diagnostic test characteristics can be performed successfully when applying multiple diagnostic tests to every individual subject, using a Bayesian approach which combines test results and external information (Berkvens et al, 2006;Adel et al, 2010;Praud et al, 2012). …”