Nonparametric hyperrectangular tolerance and prediction regions for setting multivariate reference regions in...

Area of Science:

• Clinical Chemistry
• Laboratory Medicine
• Biostatistics

Background:

• Reference regions are crucial for interpreting patient test results in clinical chemistry.
• Existing methods for univariate reference limits are well-established.
• Limited methods exist for constructing multivariate reference regions due to geometric constraints of traditional statistical regions.

Purpose of the Study:

• To develop multivariate hyperrectangular nonparametric tolerance regions for setting reference regions.
• To address the limitations of traditional multivariate statistical regions in clinical applications.
• To provide a robust method for defining reference regions in multivariate data.

Main Methods:

• Utilizes statistical data depth to identify and trim outliers.
• Employs the extremes of the trimmed dataset to define the boundaries of the hyperrectangular region.
• Incorporates a strategy for determining the optimal number of points to trim based on asymptotic results.

Main Results:

• The proposed procedure demonstrates favorable performance for moderate to large sample sizes.
• Successfully applied to establish reference regions for clinical problems.
• Provides a novel approach for constructing multivariate reference regions with hyperrectangular geometry.

Conclusions:

• The developed method offers a practical solution for creating multivariate reference regions in clinical settings.
• This approach improves the interpretation of multivariate test results in laboratory medicine.
• The procedure is effective for applications such as assessing kidney function and characterizing growth factor concentrations.