## Abstract

**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.

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