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

The goal of this work is to evaluate, with application to a real case study of the Q fever, the performances of three diagnostic tests applied to the same population, when no gold standard is available. Moreover, as in the case study we considered the situattion where there are no informations about the prevalence of the illness in the population under study. In next section, the real case study is introduced. In Section 3 we specify the theoretical assumptions and propose a possible way to estimate the parameters of interest. In Section 4 we evaluate the proposed method by a simulation study, and finally apply it to the observed data.