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A random-sum Wilcoxon statistic and its application to analysis of ROC and LROC data. (English) Zbl 1197.62045

Summary: The Wilcoxon-Mann-Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly localized abnormal images is random, while in the latter the violation is due to some subjects not having observable measurements. For this reason, we propose a random-sum Wilcoxon statistic for comparing two groups in the presence of ties, and derive its variance as well as its asymptotic distribution for large sample sizes. The proposed statistic includes the regular Wilcoxon rank-sum statistic. Finally, we apply the proposed statistic for summarizing location response operating characteristic data from a liver computed tomography study, and also for summarizing diagnostic accuracy of biomarker data.

MSC:

62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C55 Biomedical imaging and signal processing
92C50 Medical applications (general)
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