For the two-sample problem, the Wilcoxon-Mann-Whitney (WMW) test is used frequently: it is simple to explain (a permutation test on the difference in mean ranks), it handles continuous or ordinal responses, it can be implemented for large or small samples, it is robust to outliers, it requires few assumptions, and it is efficient in many cases. Unfortunately, the WMW test is rarely presented with an effect estimate and confidence interval. A natural effect parameter associated with this test is the Mann-Whitney parameter, φ = Pr[ X

Group testing has its origin in the identification of syphilis in the U.S. army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this article, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures, when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article available online.

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.

Summary Due to the rising cost of laboratory assays, it has become increasingly common in epidemiological studies to pool biospecimens. This is particularly true in longitudinal studies, where the cost of performing multiple assays over time can be prohibitive. In this article, we consider the problem of estimating the parameters of a Gaussian random effects model when the repeated outcome is subject to pooling. We consider different pooling designs for the efficient maximum likelihood estimation of variance components, with particular attention to estimating the intraclass correlation coefficient. We evaluate the efficiencies of different pooling design strategies using analytic and simulation study results. We examine the robustness of the designs to skewed distributions and consider unbalanced designs. The design methodology is illustrated with a longitudinal study of premenopausal women focusing on assessing the reproducibility of F2-isoprostane, a biomarker of oxidative stress, over the menstrual cycle.