Evaluating Sensitivity and Specificity of three Diagnostic Tests when the Gold Standard is Unavailable, with Application to the Cattle Q Fever Case Study

In the context diagnostic tests may be assessed through indicators of diagnosis reliability called specificity and sensitivity. In practice, these indicators can be estimated only if a "gold standard" test is available, meaning that its diagnosis is the most reliable one available about the prevalence of the illness in the population Starting from a real case study related to cattle Q fever, the aim of this work is to determine which is the best diagnostic test among the three examined taking into account there is neither any a priori information on the sensitivity and specificity of three tests, nor a reference "gold standard" diagnostic test. Moreover, the incidence of the disease in the reference population is unknown. Our approach, mainly descriptive in nature, derived estimates of sensitivity and specificity of the diagnostic tests according to incidence of the disease. The estimates are obtained by minimizing the least squares and a performed simulation study shows that, on average, the method provides unbiased estimated of unknown parameters. The application of the method to a real case study allows to establish a hierarchy among the three diagnostic tests in question.