ROC and loss function analysis in sequential testing

Sequential testing is applied to reduce costs in SP-based tests (OSCEs). Initially, all candidates take a screening test consisting of a part of the OSCE. Candidates who fail the screen sit the complete test, whereas those who pass the screen are qualified as a pass of the complete test. The procedure may result in a reduction of testing resources, but at the cost of false positives (candidates who pass the screen but would fail the complete test). In a diagnostic test an optimum cutpoint is obtained by minimizing the weighted sum of false negatives and false positives using Receiver Operator Characteristic (ROC) analysis. However, in the sequential procedure there are no false negatives, because the result of the complete test is considered the final outcome. Several authors ignored this difference and applied classic ROC analysis to a sequential test. Earlier, we doubted the validity of the procedure and proposed to set the cutpoint by minimizing the loss, defined as the weighted sum of the screen negatives and the false positives. Recently, Regehr and Colliver (2003) argued that under certain theoretically derived conditions the use of the loss formula in sequential testing is functionally identical to using classic ROC analysis. The current study shows (a) the conclusion of Regehr and Colliver is based on assumptions that can be challenged, and (b) ROC analysis indeed can be used in sequential testing, but only if the procedure is modified according to the results of a corresponding loss function analysis.