Estimating Test Accuracy with an Imperfect Reference
Suppose that a gold standard does not exist, but the accuracy of a new test will be assessed with an imperfect gold standard. Many cases exist where there is no perfect gold standard. For example, depression is usually determined by a series of questions and observing the behavior of the patient, but such assessments are highly subjective, and there is no one test that provides a perfect diagnosis. For infectious diseases, a perfect diagnosis can be elusive, where a culture is taken, however, the culture may not contain the infective agent or if the agent is present, it may not grow in the culture. Pepe  gives other examples, including tests for diagnosing cancer and hearing loss. Zhou, McClish, and Obuchowski  also present various studies, including the diagnosis of a bacterial infection with the stool and serology tests. The method of analysis is maximum likelihood, while the approach taken here is Bayesian. Other examples presented by Zhou, McClish, and Obuchowski include two tests for tuberculosis, with the Tine and Mantour tests, at two diﬀerent sites, while a third example for detecting pleural thickening is performed by x-ray with three readers. Pepe describes another interesting example of multiple tests, where Chlamydia bacterial infection is diagnosed with a blood culture, polymerase chain reaction (PCR), and enzyme linked immunosorbent assay (ELISA).