On dependent repeated screening tests

A screening test is applied n times to a person with known true status. If more than k tests have positive outcomes, then the person is assigned to be screen-positive; otherwise, the person is assigned to be screen-negative. Assuming that the tests are exchangeable, we can characterize the possible dependence among tests by at most n parameters called canonical moments, which can be estimated from the data. The performance characteristics of the composite test (such as likelihood ratios, sensitivity, and specificity) can be computed based on these estimates. Thus, we can choose n and k so that the desired levels of likelihood ratios, sensitivity, and specificity can be achieved. We study the cases n = 2 and n = 3 in detail.