Meta-analysis of proportions using generalized linear mixed models

Lifeng Lin, Haitao Chu

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Epidemiologic research often involves meta-analyses of proportions. Conventional two-step methods first transform each study's proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been recommended in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.

Original languageEnglish (US)
Pages (from-to)713-717
Number of pages5
Issue number5
StatePublished - Sep 1 2020

Bibliographical note

Funding Information:
Submitted January 8, 2020; accepted June 29, 2020. From the aDepartment of Statistics, Florida State University, Tallahassee, FL and bDivision of Biostatistics, School of Public Health, University of Min-nesota, Minneapolis, MN This research was supported in part by the US National Institutes of Health/ National Library of Medicine grant R01LM012982 (L.L. and H.C.) and the National Institutes of Health/National Center for Advancing Trans-lational Sciences grant UL1TR001427 (L.L.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors report no conflicts of interest. Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article ( Data and code: The datasets and code for all analyses are available in the supplemental file. Correspondence: Lifeng Lin, Department of Statistics, Florida State Univer-sity, Tallahassee, FL 32306. E-mail:

Publisher Copyright:
© 2020 Lippincott Williams and Wilkins. All rights reserved.


  • data transformation
  • generalized linear mixed model
  • link function
  • meta-analysis
  • proportion

PubMed: MeSH publication types

  • Journal Article


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