### Article

## Comparison of four estimators of the heterogeneity variance for meta-analysis

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Published: | September 6, 2007 |
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### Outline

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**Introduction:** The analysis of heterogeneity is a crucial part of each meta-analysis. In order to analyze heterogeneity often a random effects model which incorporates variation between studies is considered. It is assumed that each study has its own (true) exposure or therapy effect and that there is a random distribution of these true exposure effects around a central effect. The variability between studies is quantified by the heterogeneity variance.

**Material and methods:** In order to compare the performance of four estimators of the heterogeneity variance a simulation study was performed. This study compared the Dersimonian-Laird (1986) estimator with the maximum-likelihood estimator based on the normal distribution for the random effects. Further comparators were the simple heterogeneity (SH) variance estimator proposed by Sidek and Jonkman (2005) and an estimator based on a finite mixture model (Böhning, Dietz,and Schlattmann, 1998). The simulation study investigated bias, standard deviation and mean square error (MSE) of all four estimators.

**Results:** Based on this study it turned out that the SH estimator behaves well for almost all settings. Finite finite mixture models had the second best properties in terms of bias and mean square error. The worst performance in terms of bias had the DerSimonian-Lard estimator.

**Discussion:** The SH estimator has acceptable properties. Additionally it is easy to compute. One drawback is that it relies on the assumption of a normal distribution of the random effects. If one is in doubt regarding this assumption a finite mixture model may be considered. . However, considering ease of implementation and performance the SH estimator seems to be a good choice.

### References

- 1.
- Böhning D, Dietz E and P Schlattmann. Recent developments in computer assisted mixture analysis. Biometrics: 54: 283-303
- 2.
- DerSimonian R and N Laird. Meta-analysis in clinical trials. Controlled Clinical Trials:7:177-188
- 3.
- Sidek K and J Jonkman. Simple heterogeneity variance for meta-analysis. JRSS: Series C, 54: 367-384.