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Rectangular multivariate normal prediction regions for setting reference regions in laboratory medicine.

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Rectangular tolerance regions and multivariate normal reference regions in laboratory medicine.

Michael Daniel Lucagbo1,2, Thomas Mathew1

  • 1Department of Mathematics & Statistics, University of Maryland Baltimore County, Baltimore, Maryland, USA.

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|October 26, 2022
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Summary
This summary is machine-generated.

This study introduces rectangular reference regions for multivariate data, improving upon traditional ellipsoidal methods. These new regions enhance specificity and detect component-wise extremes in patient test results.

Keywords:
central tolerance intervalsmixed reference intervalsparametric bootstrapsimultaneous tolerance intervals

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Area of Science:

  • Biostatistics
  • Clinical Chemistry
  • Medical Diagnostics

Background:

  • Reference intervals are crucial for interpreting patient test results.
  • Multivariate reference regions are superior to univariate intervals for multiple analytes, accounting for variable correlations.
  • Traditional ellipsoidal regions fail to detect component-wise extreme observations.

Purpose of the Study:

  • To develop procedures for constructing rectangular reference regions under multivariate normality.
  • To address the computation of rectangular tolerance regions and simultaneous tolerance intervals.
  • To compute mixed reference intervals with both two-sided and one-sided limits.

Main Methods:

  • Construction of rectangular reference regions based on tolerance interval criteria.
  • Utilized a parametric bootstrap approach for computations.
  • Assessed methodology accuracy using estimated coverage probabilities and addressed sample size determination.

Main Results:

  • Developed procedures for computing rectangular reference regions in multivariate normal distributions.
  • Successfully computed simultaneous and mixed reference intervals.
  • Demonstrated the accuracy and applicability of the proposed methodology through examples.

Conclusions:

  • Rectangular reference regions offer improved specificity and detection of component-wise extremes compared to ellipsoidal methods.
  • The proposed parametric bootstrap approach provides accurate computations for these regions.
  • This methodology is valuable for interpreting multivariate patient test results.