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Clinical Chemistry and Laboratory Medicine (CCLM)

Published in Association with the European Federation of Clinical Chemistry and Laboratory Medicine (EFLM)

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In This Section
Volume 46, Issue 12 (Dec 2008)


Introduction of non-linearity by data transformation in method comparison and commutability studies

Dietmar Stöckl
  • 1Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium
/ Linda M. Thienpont
  • 2Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium
Published Online: 2008-10-31 | DOI: https://doi.org/10.1515/CCLM.2008.342


Background: Logarithmic transformation is recommended in method comparison or commutability studies when the standard deviation of the measurement results is heteroscedastic. We show that in the case of a considerable constant difference in the relationship between the x- and y-data, logarithmic transformation introduces non-linearity.

Methods: We used a simulated bivariate dataset [n=50; no systematic differences between the x- and y-data; x-data without error and y-data with concentration-dependent random, normally distributed error (CV=7%)], from which we generated two new sets of data: one by i) multiplying the y-data by 1.1, and the second by ii) adding a constant value of 15 to the y-data.

Results: The runs test (p<0.001) confirms that logarithmic transformation of the second dataset introduces non-linearity. Consequently, applying a linear regression model to the transformed data would result in erroneous decisions about commutability and in erroneously high estimates of the limits of agreement in method comparison studies.

Conclusions: We recommend applying a linearity test after logarithmic transformation of bivariate data and, if necessary, to calculate the prediction intervals of a non-linear regression function.

Clin Chem Lab Med 2008;46:1784–5.

Keywords: heteroscedastic; logarithmic (ln) transformation; standard deviation

About the article

Corresponding author: Linda M. Thienpont, Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Harelbekestraat 72, 9000 Gent, Belgium Phone: +32-9-2648104, Fax: +32-9-2648198,

Received: 2008-06-27

Accepted: 2008-08-12

Published Online: 2008-10-31

Published in Print: 2008-12-01

Citation Information: Clinical Chemistry and Laboratory Medicine, ISSN (Online) 1437-4331, ISSN (Print) 1434-6621, DOI: https://doi.org/10.1515/CCLM.2008.342.

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©2008 by Walter de Gruyter Berlin New York. Copyright Clearance Center

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