Abstract:
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Reference regions are widely used in clinical chemistry and laboratory medicine to interpret the results of biochemical or physiological tests of patients. There are well-established methods in the literature for reference limits for univariate measurements, however, only limited methods are available for the construction of multivariate reference regions. This is because traditional multivariate statistical regions (e.g., confidence, prediction, and tolerance regions) are not constructed based on a hyperrectangular geometry. We address this problem by developing multivariate hyperrectangular nonparametric tolerance regions for setting the reference regions. Our approach uses statistical data depth to determine which points to trim and then the extremes of the trimmed dataset are used as the faces of the hyperrectangular region. We also specify the number of points to trim based on previously-established asymptotic results. An extensive coverage study shows the favorable performance of our algorithm for moderate to large sample sizes. We apply our procedure to a healthy reference sample to obtain reference regions for three analytes pertaining to kidney function.
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