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Clinical Chemistry and Laboratory Medicine (CCLM)

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

Editor-in-Chief: Plebani, Mario

Ed. by Gillery, Philippe / Lackner, Karl J. / Lippi, Giuseppe / Melichar, Bohuslav / Schlattmann, Peter / Tate, Jillian R. / Tsongalis, Gregory J.

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

Dietmar Stöckl1 / Linda M. Thienpont2

1Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium

2Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium

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,

Citation Information: Clinical Chemistry and Laboratory Medicine. Volume 46, Issue 12, Pages 1784–1785, ISSN (Online) 1437-4331, ISSN (Print) 1434-6621, DOI: 10.1515/CCLM.2008.342, October 2008

Publication History

Published Online:


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

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