The Bland-Altman method, which assesses agreement via an assessment set constructed by the difference of the measurement variables, has received great attention. Other assessment approaches have been proposed following the same difference-based framework. However, the exact assessment set constructed by the difference is achievable only for measurements with certain joint distributions. To provide a more general assessment framework, we propose two approaches. First, when the measurement distribution is known, we propose a parametric approach that constructs the assessment set through a measure of closeness corresponding to the distribution. Second, when the measurement distribution is unknown, we propose a nonparametric approach that constructs the assessment set through quantile regression. Both approaches quantify the degree of agreement with the presence of both systematic and random measurement errors, and enable one to go beyond the difference-based approach. Results of simulation and data analyses are presented to compare the two approaches.

The objective of this article is to propose and study frequentist tests that have maximum average power, averaging with respect to some specified weight function. First, some relationships between these tests, called maximum average-power (MAP) tests, and most powerful or uniformly most powerful tests are presented. Second, the existence of a maximum average-power test for any hypothesis testing problem is shown. Third, an MAP test for any hypothesis testing problem with a simple null hypothesis is constructed, including some interesting classical examples. Fourth, an MAP test for a hypothesis testing problem with a composite null hypothesis is discussed. From any one-parameter exponential family, a commonly used UMPU test is shown to be also an MAP test with respect to a rich class of weight functions. Finally, some remarks are given to conclude the article.

SUMMARYOutlier sums were proposed by Tibshirani & Hastie (2007) and Wu (2007) for detecting outlier genes where only a small subset of disease samples shows unusually high gene expression, but they did not develop their distributional properties and formal statistical inference. In this study, a new outlier sum for detection of outlier genes is proposed, its asymptotic distribution theory is developed, and the p-value based on this outlier sum is formulated. Its analytic form is derived on the basis of the large-sample theory. We compare the proposed method with existing outlier sum methods by power comparisons. Our method is applied to DNA microarray data from samples of primary breast tumors examined by Huang et al. (2003). The results show that the proposed method is more efficient in detecting outlier genes.

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