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

Wei Liu1, Frank Bretz2, Mario Cortina-Borja3

  • 1Southampton Statistical Sciences Research Institute and School of Maths, University of Southampton, Southampton, SO17 1BJ, UK.

Statistics in Medicine
|February 12, 2024
PubMed
Summary

Nonparametric hyperrectangular tolerance regions offer robust interpretation of laboratory test results. Mathematical proofs confirm their validity for continuous measurements, enhancing diagnostic accuracy in medicine.

Keywords:
nonparametric tolerance intervalnonparametric tolerance regionreference rangereference regiontolerance intervaltolerance region

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Area of Science:

  • Statistics
  • Medical Laboratory Science
  • Biostatistics

Background:

  • Reference regions are crucial for interpreting patient test results in laboratory medicine.
  • Tolerance regions are commonly used, with hyperrectangular regions being particularly useful for multiple outcome measures.
  • Existing methods for nonparametric hyperrectangular tolerance regions lack rigorous mathematical validation.

Purpose of the Study:

  • To develop and mathematically validate nonparametric hyperrectangular tolerance regions.
  • To provide a robust method for constructing tolerance regions applicable to continuous measurement distributions.
  • To apply the validated methodology to a real-world kidney function analysis.

Main Methods:

  • Utilizing Tukey's equivalence blocks to construct nonparametric hyperrectangular tolerance regions.
  • Providing mathematical proofs for the validity of these tolerance regions under the assumption of continuous data.
  • Applying the constructed regions to analyze kidney function data.

Main Results:

  • New nonparametric hyperrectangular tolerance regions were constructed using Tukey's equivalence blocks.
  • The mathematical validity of these tolerance regions was rigorously proven for continuous measurement distributions.
  • The methodology was successfully applied to analyze kidney function, demonstrating practical utility.

Conclusions:

  • The study provides mathematically validated nonparametric hyperrectangular tolerance regions.
  • This method offers a robust and interpretable approach for establishing reference regions in laboratory medicine.
  • The findings have significant implications for the accurate interpretation of diagnostic tests, particularly those with multiple outcome measures.