Undue reliance on I(2) in assessing heterogeneity may mislead

Abstract

Background: The heterogeneity statistic I(2), interpreted as the percentage of variability due to heterogeneity between studies rather than sampling error, depends on precision, that is, the size of the studies included.

Methods: Based on a real meta-analysis, we simulate artificially 'inflating' the sample size under the random effects model. For a given inflation factor M = 1, 2, 3,... and for each trial i, we create a M-inflated trial by drawing a treatment effect estimate from the random effects model, using s(i)(2)/M as within-trial sampling variance.

Results: As precision increases, while estimates of the heterogeneity variance tau(2) remain unchanged on average, estimates of I(2) increase rapidly to nearly 100%. A similar phenomenon is apparent in a sample of 157 meta-analyses.

Conclusion: When deciding whether or not to pool treatment estimates in a meta-analysis, the yard-stick should be the clinical relevance of any heterogeneity present. tau(2), rather than I(2), is the appropriate measure for this purpose.

Figure 1

Top left panel: Meta-analysis of thrombolytic therapy in acute myocardial infarction [14]. Other plots: illustrative randomly sampled versions of the same meta-analysis with sample-size inflation factors of M = 4, 16 and 64 (details in text).

Figure 2

Within-study variation, decreasing with increasing sample size while heterogeneity remains constant. Details in text.

Figure 3

Percentage I² of variation due to heterogeneity rather than to sampling error against sample size (same simulation data as in Figure 2).

Figure 4

I² against median study size in a sample of 157 meta-analyses. Light, grey and black dots and regression lines correspond to the first, second and third tercile of the distribution of τ².