Comparing dichotomous screening tests when individuals negative on both tests are not verified

Two dichotomous screening tests are often compared by performing both tests in a sampled population, and submitting positive results on either test to verification by the reference standard. Unbiased estimates of the true positive and false positive rates of each test cannot be estimated directly. However, unbiased estimates of the relative true positive and relative false positive rates may be obtained. When one test has a higher true positive rate at the expense of a higher false positive rate, the trade off is represented by the ratio of extra false positives detected to extra true positives detected. A 95% confidence interval for this ratio is derived. This ratio is prevalence dependent and only applies to the sampled population. For target populations of different prevalence, estimates of the ratio may be obtained if one of the following applies: (i) the test characteristics of one test are known; (ii) the relative prevalence is known; and (iii) certain assumptions are made.