Evaluating sensitivity and specificity of three diagnostic tests when the “gold standard” is unavailable,

Abstract

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 as to the prevalence of an illness in a population. Starting from a real case study related to cattle Q fever disease in small ruminants, the aim of this work is to determine which of the three examined diagnostic tests is the best, taking into account the fact that there is neither any a priori information on the sensitivity and specificity of the three tests, nor a reference “gold standard” diagnostic test. Moreover, the incidence of the disease in the reference population is unknown. Our approach, which is mainly descriptive in nature, derived estimates of sensitivity and specificity of the diagnostic tests from 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 estimates of unknown parameters. The application of the method to a real case study make it possible to establish a hierarchy among the three diagnostic tests in question.