Reader reaction: A note on the evaluation of group testing algorithms in the presence of misclassification

In the context of group testing screening, McMahan, Tebbs, and Bilder (2012, Biometrics 68, 287-296) proposed a two-stage procedure in a heterogenous population in the presence of misclassification. In earlier work published in Biometrics, Kim, Hudgens, Dreyfuss, Westreich, and Pilcher (2007, Biometrics 63, 1152-1162) also proposed group testing algorithms in a homogeneous population with misclassification. In both cases, the authors evaluated performance of the algorithms based on the expected number of tests per person, with the optimal design being defined by minimizing this quantity. The purpose of this article is to show that although the expected number of tests per person is an appropriate evaluation criteria for group testing when there is no misclassification, it may be problematic when there is misclassification. Specifically, a valid criterion needs to take into account the amount of correct classification and not just the number of tests. We propose, a more suitable objective function that accounts for not only the expected number of tests, but also the expected number of correct classifications. We then show how using this objective function that accounts for correct classification is important for design when considering group testing under misclassification. We also present novel analytical results which characterize the optimal Dorfman (1943) design under the misclassification.