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Estimation of reference ranges from normal samples.

P Royston1, J N Matthews

  • 1Department of Medical Physics, Royal Postgraduate Medical School (University of London), U.K.

Statistics in Medicine
|May 1, 1991
PubMed
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This study explores statistical methods for medical reference ranges, proposing that estimating symmetric centiles of the normal distribution offers practical advantages over traditional mean ± two standard deviations. This approach enhances the reliability of clinical reference intervals.

Area of Science:

  • Medical Statistics
  • Clinical Laboratory Science

Background:

  • Reference ranges are crucial in medicine, often calculated as mean ± two standard deviations.
  • The statistical basis for these ranges is frequently debated and subject to interpretation.
  • Current methods may use the Student t distribution to achieve nominal coverage (e.g., 95% or 99%).

Purpose of the Study:

  • To investigate alternative statistical methods for calculating medical reference ranges.
  • To advocate for a method based on estimating symmetric centiles of the normal distribution.
  • To provide practical formulas for this proposed method.

Main Methods:

  • Statistical analysis focusing on the normal distribution.
  • Estimation of symmetric centiles.
  • Comparison with traditional methods like mean ± two standard deviations and Student t distribution.

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Main Results:

  • A case is made for using reference ranges derived from symmetric centile estimation.
  • Formulas for calculating these ranges are provided.
  • The simplest estimator (sample mean ± normal-based SDs) demonstrates theoretical and practical benefits.

Conclusions:

  • Estimating symmetric centiles provides a statistically robust foundation for medical reference ranges.
  • The proposed method offers advantages over conventional approaches.
  • This approach can improve the accuracy and interpretation of clinical reference intervals.