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

Stöckl, Dietmar
Thienpont, Linda M.

Laboratory 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, E-mail: [email protected]

Received June 27, 2008; accepted August 12, 2008; previously published online October 31, 2008

Clinical Chemistry and Laboratory Medicine 46(12):p 1784-1785, December 2008.

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%)x, 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.