Analytic methods for comparing two dichotomous screening or diagnostic tests applied to two populations of differing disease prevalence when individuals negative on both tests are unverified

Two dichotomous screening tests may be compared by applying both tests to all members of a sampled population. For individuals with a positive result on either test the disease status may be verified by a reference standard, but for individuals negative on both tests the disease status may be unverified because the probability of disease is so low that further investigation is costly, unacceptable and perhaps unethical. If the tests have been applied to samples from two populations which have different disease prevalences then unbiased estimates of the true positive and false positive rates of each test, the prevalences in the two populations, and two parameters representing dependence between the two tests can be estimated using maximum likelihood methods. The methods are based on the assumption that the sensitivities and specificities of the two tests, and the dependencies between the tests, are independent of prevalence. A test of goodness of fit provides a test of this.