Abstract
The practice of sequential testing is followed by the evaluation of accuracy, but not by the evaluation of cost. This paper focuses on three logic rules for combining two sequences of tests: believe the positive (BP), which diagnoses disease if any of two tests is positive, believe the negative (BN), which diagnoses disease if any of two tests is negative, and believe the extreme (BE), which diagnoses disease if the first test is positive or, after a first inconclusive test, a second test is positive for disease. Comparisons of these strategies are provided in terms of accuracy using false positive rate, sensitivity pairs that make up the maximum receiver operating characteristic curve, and cost of testing, defined as the proportion of subjects needing two tests to diagnose disease. A method to incorporate the cost of testing into the definition of the optimal operating point is also presented. The performance of the testing strategies is examined with respect to the ratio of standard deviations and the correlation between test results under the bivariate normal assumptions. Under all parameter settings, the maximum receiver operating characteristic curve of the BE strategy never performed worse than the BN and BP strategies; the BE strategy also had the lowest cost. The use of body mass index and plasma glucose concentration to diagnose diabetes in Pima Indians was presented as a real-world application. The optimal operating points found by the BN and BE strategies produce lower false positive rate values than the BP strategy for these data. Copyright (C) 2011 John Wiley & Sons, Ltd.