A comparison of 20 heterogeneity variance estimators in statistical synthesis of results from studies: a simulation study

Stat Med. 2017 Nov 30;36(27):4266-4280. doi: 10.1002/sim.7431. Epub 2017 Aug 16.


When we synthesize research findings via meta-analysis, it is common to assume that the true underlying effect differs across studies. Total variability consists of the within-study and between-study variances (heterogeneity). There have been established measures, such as I2 , to quantify the proportion of the total variation attributed to heterogeneity. There is a plethora of estimation methods available for estimating heterogeneity. The widely used DerSimonian and Laird estimation method has been challenged, but knowledge of the overall performance of heterogeneity estimators is incomplete. We identified 20 heterogeneity estimators in the literature and evaluated their performance in terms of mean absolute estimation error, coverage probability, and length of the confidence interval for the summary effect via a simulation study. Although previous simulation studies have suggested the Paule-Mandel estimator, it has not been compared with all the available estimators. For dichotomous outcomes, estimating heterogeneity through Markov chain Monte Carlo is a good choice if an informative prior distribution for heterogeneity is employed (eg, by published Cochrane reviews). Nonparametric bootstrap and positive DerSimonian and Laird perform well for all assessment criteria for both dichotomous and continuous outcomes. Hartung-Makambi estimator can be the best choice when the heterogeneity values are close to 0.07 for dichotomous outcomes and medium heterogeneity values (0.01 , 0.05) for continuous outcomes. Hence, there are heterogeneity estimators (nonparametric bootstrap DerSimonian and Laird and positive DerSimonian and Laird) that perform better than the suggested Paule-Mandel. Maximum likelihood provides the best performance for both types of outcome in the absence of heterogeneity.

Keywords: coverage probability; heterogeneity variance estimators; length of confidence interval; mean absolute estimation error; simulation study.

Publication types

  • Comparative Study

MeSH terms

  • Computer Simulation
  • Data Interpretation, Statistical*
  • Humans
  • Markov Chains
  • Meta-Analysis as Topic*
  • Monte Carlo Method
  • Statistics as Topic