We address the comparison of results between two diagnostic tests applied multiple times to the same subjects. The estimand of interest is the sensitivity of the combined test (primary and adjunct) relative to a primary test. Analytical methods are first described that assume independence between the multiple observations within a subject. In order to account for the within-subject correlation introduced by the multiple measurements, analytical approaches for correlated, categorical response data are described. In the discussion of these methods, we pay particular attention to the presence of a structural zero which results from the decision rule for the combination of diagnostic tests. In a simulation study, we compare the finite sample performances of all analytical approaches in terms of confidence interval coverage rates and median lengths. Our methods are cast in the context of a diagnostic bronchoscopy technology for the detection of lung cancer.