Comparing diagnostic tests on benefit-risk

Comparing diagnostic tests on accuracy alone can be inconclusive. For example, a test may have better sensitivity than another test yet worse specificity. Comparing tests on benefit risk may be more conclusive because clinical consequences of diagnostic error are considered. For benefit-risk evaluation, we propose diagnostic yield, the expected distribution of subjects with true positive, false positive, true negative, and false negative test results in a hypothetical population. We construct a table of diagnostic yield that includes the number of false positive subjects experiencing adverse consequences from unnecessary work-up. We then develop a decision theory for evaluating tests. The theory provides additional interpretation to quantities in the diagnostic yield table. It also indicates that the expected utility of a test relative to a perfect test is a weighted accuracy measure, the average of sensitivity and specificity weighted for prevalence and relative importance of false positive and false negative testing errors, also interpretable as the cost-benefit ratio of treating non-diseased and diseased subjects. We propose plots of diagnostic yield, weighted accuracy, and relative net benefit of tests as functions of prevalence or cost-benefit ratio. Concepts are illustrated with hypothetical screening tests for colorectal cancer with test positive subjects being referred to colonoscopy.