Back-transformation of treatment differences—an approximate method

Abstract

Background/Objectives:

Transformation of outcomes is frequently used in the analysis of studies in clinical nutrition. However, back-transformation of estimated treatment means and differences is complicated by the nonlinear nature of the transformations. It is not straightforward to obtain an estimated treatment difference that can be interpreted without any reference to the additional predictors included in the statistical model; and moreover, standard errors are not easily available. The aim of this work was to provide a generally applicable, yet operational procedure for obtaining back-transformed estimated differences, and corresponding standard errors and 95% confidence intervals.

Subjects/Methods:

Based on data from two randomized controlled studies and an exemplary data set that had all previously been published, we evaluated our approximate procedure by comparing results for different approaches for showing back-transformed estimated treatment differences.

Results:

Estimated differences obtained on logarithm, square root and reciprocal square root-transformed scales were back-transformed into estimated differences on the original scales, and these estimates were in good agreement with the results reported by the original studies.

Conclusions:

The proposed approximate procedure provides a flexible approach for obtaining quite accurate back-transformed estimated differences in terms of medians and for deriving the corresponding standard errors.