Distribution-free hyperrectangular tolerance regions for setting multivariate reference regions in laboratory medicine

Liu, Wei, Bretz, Frank and Cortina-Borja, Mario (2023) Distribution-free hyperrectangular tolerance regions for setting multivariate reference regions in laboratory medicine. Statistics in Medicine. (In Press)

Record type: Article

Abstract

Reference regions are important in laboratory medicine to interpret the test results of patients, and usually given by tolerance regions. Tolerance regions of p (>= 2) dimensions are highly desirable when the test results contains p outcome measures. Nonparametric hyperrectangular tolerance regions are attractive in real problems due to their robustness with respect to the underlying distribution of the measurements and ease of intepretation, and methods to construct them have been recently provided by Young and Mathew [1]. However, their validity is supported by a simulation study only. In this paper, nonparametric hyperrectangular tolerance regions are constructed by using Tukey's [2,3] elegant results of equivalence blocks. The validity of these new tolerance regions is proven mathematically in [2,3] under the only assumption that the underlying distribution of the measurements is continuous. The methodology is applied to analyze the kidney function problem considered in Young and Mathew [1]

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Distribution-free hyperrectangular tolerance regions for setting multivariate reference regions in laboratory medicine - Accepted Manuscript

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