Differential diagnosis in immunohistochemistry with Bayes theorem

When immunohistochemical stains that are specific for specific tumor diagnoses do not yield diagnostic results, we often turn to less specific immunohistochemical stains and consider the resulting lists of possible tumor types. Typically, such lists are ordered according to tumor sensitivities for the stains. In probability terminology, sensitivity is the conditional probability of a positive stain given a specific tumor. Yet, the most useful probability to know is the probability of a specific tumor diagnosis, given a set of staining results. Bayes theorem provides this probability. To illustrate its use for differential diagnosis, I apply it here to the situation of carcinomas of uncertain primary site and use the information provided by stains for cytokeratin 7 and cytokeratin 20.