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Updated: May 16, 2026

The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials
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The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials

Published on: April 19, 2024

Back-transformations in random-effects meta-analysis-Impact and interpretation.

Jan-Bernd Igelmann1, Markus Pauly1,2, Wolfgang Viechtbauer3

  • 1Department of Statistics, https://ror.org/01k97gp34TU Dortmund University, Germany.

Research Synthesis Methods
|May 15, 2026
PubMed
Summary
This summary is machine-generated.

Standard inverse back-transformations in meta-analysis estimate medians, not means. Integral back-transformations can recover mean effect sizes but require careful application due to potential instability and sensitivity to heterogeneity.

Keywords:
back-transformationintegral transformationmeta-analysisrandom-effects modeltransformation bias

Related Experiment Videos

Last Updated: May 16, 2026

The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials
08:36

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Published on: April 19, 2024

Area of Science:

  • Biostatistics
  • Quantitative Synthesis
  • Statistical Modeling

Background:

  • Meta-analyses often transform effect sizes for normality assumptions.
  • Back-transformation is used for interpreting results on the original scale.
  • Standard inverse back-transformations in random-effects models can yield median, not mean, estimates due to Jensen's inequality.

Purpose of the Study:

  • To investigate integral back-transformations for recovering mean effect sizes in meta-analysis.
  • To derive general formulations for integral back-transformations and confidence intervals (CIs).
  • To provide a software implementation for these methods.

Main Methods:

  • Studied integral back-transformations for various effect sizes (correlation coefficients, proportions, odds ratios, risk ratios, Cronbach's alpha).
  • Derived general formulations for integral back-transformations and associated CIs.
  • Developed a software implementation for practical application.

Main Results:

  • Integral back-transformations can recover mean effect size estimates but are sensitive to heterogeneity estimation and can be unstable.
  • Asymmetric transformations may lead to inconsistent inference.
  • Standard inverse back-transformation is suitable for descriptive purposes and median estimation.

Conclusions:

  • The choice of back-transformation method depends on the analyst's objective (mean vs. median estimation).
  • Integral back-transformation is recommended only when a mean estimate is explicitly required.
  • Use integral back-transformations for CIs cautiously, primarily for estimation, not hypothesis testing.