Back-transformation of treatment differences—an approximate method

• Published in: European journal of clinical nutrition Vol. 68; no. 2; pp. 277 - 280
• Main Authors: Laursen, R P, Dalskov, S-M, Damsgaard, C T, Ritz, C
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.02.2014; Nature Publishing Group
• Subjects: 631/114/2415; 692/700/2814; Animals; Approximation; Biological and medical sciences; Clinical Nutrition; Confidence Intervals; Cytokines - blood; Data Interpretation, Statistical; Denmark; Dietary Supplements; Epidemiology; Errors; Feeding. Feeding behavior; Fish Oils - administration & dosage; Fundamental and applied biological sciences. Psychology; Humans; Immunity - drug effects; Infant; Infant Formula; Internal Medicine; Mathematical models; Medical sciences; Medicine; Medicine & Public Health; Metabolic Diseases; Methods; Milk; Nutrition; Nutrition therapy; original-article; Outcome and process assessment (Health Care); Parametric statistics; Product/Service Evaluations; Public Health; Randomized Controlled Trials as Topic; Skinfold Thickness; Statistical analysis; Statistical models; Statistics as Topic - methods; Transformations; Treatment Outcome; Vertebrates: anatomy and physiology, studies on body, several organs or systems; Denmark; parametric models; delta method; logarithm transformation; statistics; Treatment; Metabolic diseases; Models; Comparative study
• ISSN: 0954-3007; 1476-5640; 1476-5640
• DOI: 10.1038/ejcn.2013.259

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.