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We consider the problem of comparing two diagnostic tests based on a sampleof paired test results without true state determinations, in cases where thesecond test can reasonably be assumed to be at least as specific as the first.For such cases, we provide two informative confidence bounds: A lower one forthe prevalence times the sensitivity gain of the second test with respect tothe first, and an upper one for the sensitivity of the first test. Neitherconditional independence of the two tests nor perfectness of any of them needsto be assumd.  An application of the proposed confidence bounds to a sample of 256 pairs oflaboratory test results for toxigenic Clostridium difficile provides evidencefor a dramatic sensitivity gain through first appropriately culturingClostridium difficile from stool samples before applying anenzyme-immuno-assay.

Confidence bounds for the sensitivity lack of a less specific diagnostic test, without gold standard