Limits of Agreement Based on Transformed Measurements

Method comparison studies are typically analyzed using limits of agreement (LoAs). The standard Bland–Altman approach estimates LoAs under the assumption that the differences between methods follow a normal distribution. However, many types of measurements, such as volume, concentration, and percentage values, often deviate from normality. This study explores LoAs for the difference between two clinical measurements and prediction intervals for one measurement given the other, using a transformation of the data. After back-transforming, the resulting LoA for the original measurements depends on the subject level, represented by the average of the measurements. A simulation study evaluates the statistical properties of these LoAs and their confidence limits, demonstrating strong performance for small-to-medium sample sizes. LoA derived from transformed measurements are also compared with those obtained using a regression-based method proposed by Bland and Altman. Two applications demonstrate the approach using logarithmic and cube root transformations. This transformation-based method offers a straightforward way to obtain LoAs that depends on the subject level.