Diagnosis using predictive probabilities without cut-offs

Standard diagnostic test procedures involve dichotomization of serologic test results. The critical value or cut-off is determined to optimize a trade off between sensitivity and specificity of the resulting test. When sampled units from a population are tested, they are allocated as either infected or not according to the test outcome. Units with values high above the cut-off are treated the same as units with values just barely above the cut-off, and similarly for values below the cut-off. There is an inherent information loss in dichotomization. We thus develop a diagnostic screening method based on data that are not dichotomized within the Bayesian paradigm. Our method determines the predictive probability of infection for each individual in a sample based on having observed a specific serologic test result and provides inferences about the prevalence of infection in the population sampled. Our fully Bayesian method is briefly compared with a previously developed frequentist method. We illustrate the methodology with serologic data that have been previously analysed in the veterinary literature, and also discuss applications to screening for disease in humans. The method applies more generally to a variation of the classic parametric 2-population discriminant analysis problem. Here, in addition to training data, additional units are sampled and the goal is to determine their population status, and the prevalence(s) of the subpopulation(s) from which they were sampled.