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.

An epidemiological study of Trypanosoma evansi ( T. evansi ) infection in dromedaries was conducted in four wilayate (localities) of Southern Algeria: Béchar, El Bayadh, Ouargla, Tamanrasset. Between February 2014 and April 2016, 1056 camels of different ages and both sexes from 84 herds were sampled. The prevalence was determined through parasitological examination (Giemsa stained thin smear, GST), serological tests (CATT/ T. evansi , ELISA/VSG RoTat 1.2, immune trypanolysis), and molecular tests ( T. evansi type A specific RoTat 1.2 PCR and T. evansi type B specific EVAB PCR). The overall prevalence was 2.4 % with GST, 32.4% with CATT/ T. evansi , 23.1% with ELISA/VSG RoTat 1.2, 21.0% with immune trypanolysis (TL), 11.2 % with RoTat 1.2 PCR and 0% with EVAB PCR. El Bayadh was the most affected wilaya with 11.8% positives in GST, 74.9% in CATT/ T. evansi , 70.1% in ELISA/VSG RoTat 1.2 and 62.2% in immune trypanolysis. Only in Béchar, a non-significantly higher prevalence (13.6%) was observed with RoTat1.2 PCR than in El Bayadh (13.0%). We didn't find any evidence of the presence of T. evansi type B in the study area.

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