Comparison of the Accuracy of Two Tests with a Confirmatory Procedure Limited to Positive Results

Sensitivity (S) and specificity (F) of a test can be estimated in a study only if the disease status of all subjects is independently confirmed using a gold standard. A confirmatory procedure, however, rarely is administered to all subjects, and studies comparing two tests often restrict confirmation to subjects classified as positive by either test. In this context, the parameters of interest (S1, S2, F1, and F2) cannot be estimated directly. Two useful comparative measures of accuracy that can be estimated in this design are the relative sensitivity (RSN, S1/S2) and the relative false-positive rate [RFP, (1 - F1)/(1 - F2)]. The comparison of the two tests can be regarded as a self-matched study in which each observation consists of a pair of test results. Common statistical techniques for matched data analysis can be used to make inferences about RSN and REP. A variance estimator developed for the log-risk ratio in a matched cohort study can be applied to estimate confidence intervals for RSN and RFP. In addition, conditional logistic regression is useful to test hypotheses about RSN and RFP and to assess the impact of multiple potential modifiers of RSN and RFP.