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Abstract:
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Reference regions are invaluable in the interpretation of results of biochemical and physiological tests of patients. Moreover, when there are multiple biochemical analytes measured from each subject, a multivariate reference region is called for. Because of their greater specificity against false positives, such reference regions are more desirable than multiple univariate reference regions that disregard the cross-correlations between variables. Traditionally, multivariate reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect if an observation on a specific analyte is an outlier. For this reason, we develop procedures to construct a rectangular reference region both in a multivariate normal setup and in a nonparametric setup where the measurements can be transformed to normality or symmetry. We focus on prediction regions to be used as reference regions. The approach makes use of the bootstrap to estimate the prediction factor. The results show good coverage, even for small sample sizes and large dimensions.
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