title: Introduction of non-linearity by data transformation in method comparison and commutability studies.
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.
authors.affiliation: Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium.
authors.forename: Dietmar
authors.initials: D
authors.lastname: Stöckl
authors.forename: Linda M
authors.initials: LM
authors.lastname: Thienpont
mesh_terms: D003198:Computer Simulation; D012016:Reference Values; D012044:Regression Analysis; D012107:Research Design / Q000706:statistics & numerical data*