Sensitivity and specificity of a single diagnostic test in the presence of work-up bias

Abstract

A diagnostic test is put into routine use by being applied to a population with unknown test status and unknown disease status. All subjects with a positive test are then referred to a “gold standard” assessment for the disease. Subjects with a negative test are normally not referred to the “gold standard” assessment. In some cases, the investigators may refer a small random sample of subjects with a negative test to the “gold standard” assessment in order to determine if they really do not have the disease. If “gold standard” results are not available on an entire population, it is well-known that work-up bias, or sequential-ordering bias, exists. In this situation, classical equations for sensitivity and specificity give biased results. This paper describes an equation for estimation of prevalence, and two new equations which calculate sensitivity and specificity from prevalence and predictive values, and which are appropriate for data from this type of “irregular observational design”.