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Stat Med. 2016 Sep 20;35(21):3661-75. doi: 10.1002/sim.6980. Epub 2016 May 10.

A new measure of between-studies heterogeneity in meta-analysis.

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Department of Public Health Sciences, Karolinska Institutet, Stockholm, Sweden.
Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA, U.S.A.
Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, U.S.A.
Department of Nutrition, Harvard T.H. Chan School of Public Health, Boston, MA, U.S.A.


Assessing the magnitude of heterogeneity in a meta-analysis is important for determining the appropriateness of combining results. The most popular measure of heterogeneity, I(2) , was derived under an assumption of homogeneity of the within-study variances, which is almost never true, and the alternative estimator, R^I, uses the harmonic mean to estimate the average of the within-study variances, which may also lead to bias. This paper thus presents a new measure for quantifying the extent to which the variance of the pooled random-effects estimator is due to between-studies variation, R^b, that overcomes the limitations of the previous approach. We show that this measure estimates the expected value of the proportion of total variance due to between-studies variation and we present its point and interval estimators. The performance of all three heterogeneity measures is evaluated in an extensive simulation study. A negative bias for R^b was observed when the number of studies was very small and became negligible as the number of studies increased, while R^I and I(2) showed a tendency to overestimate the impact of heterogeneity. The coverage of confidence intervals based upon R^b was good across different simulation scenarios but was substantially lower for R^I and I(2) , especially for high values of heterogeneity and when a large number of studies were included in the meta-analysis. The proposed measure is implemented in a user-friendly function available for routine use in r and sas. R^b will be useful in quantifying the magnitude of heterogeneity in meta-analysis and should supplement the p-value for the test of heterogeneity obtained from the Q test.


heterogeneity; meta-analysis; random-effects

[Indexed for MEDLINE]

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