Estimation of test sensitivity and specificity when disease confirmation is limited to positive results

Estimation of sensitivity and specificity for diagnostic or screening tests usually requires independent confirmation of subjects as diseased or nondiseased using a gold standard. In practice, however, application of the confirmatory procedure is usually limited to individuals with one or more positive test results. For situations in which two initial tests are applied, recent literature has shown that one can use the data from confirmed disease cases to estimate the ratio of test sensitivities and the information from confirmed noncases to estimate the ratio of false-positive rates. In this paper, I show that estimates of sensitivity and specificity can be obtained for each test separately, together with an estimate of the disease prevalence. The only additional information required compared with previous methodology is the total number of individuals tested, a quantity that is usually readily available. The assumption that the test errors are independent is required. Although specific patterns of test errors cannot be identified, the overall assumption can be tested using goodness of fit. I illustrate the methods using data on breast cancer screening. Provision of sensitivity and specificity estimates for each test separately provide considerably greater insight into the data than previous methods.