A re-analysis of the Cochrane Library data: the dangers of unobserved heterogeneity in meta-analyses

Abstract

Background: Heterogeneity has a key role in meta-analysis methods and can greatly affect conclusions. However, true levels of heterogeneity are unknown and often researchers assume homogeneity. We aim to: a) investigate the prevalence of unobserved heterogeneity and the validity of the assumption of homogeneity; b) assess the performance of various meta-analysis methods; c) apply the findings to published meta-analyses.

Methods and findings: We accessed 57,397 meta-analyses, available in the Cochrane Library in August 2012. Using simulated data we assessed the performance of various meta-analysis methods in different scenarios. The prevalence of a zero heterogeneity estimate in the simulated scenarios was compared with that in the Cochrane data, to estimate the degree of unobserved heterogeneity in the latter. We re-analysed all meta-analyses using all methods and assessed the sensitivity of the statistical conclusions. Levels of unobserved heterogeneity in the Cochrane data appeared to be high, especially for small meta-analyses. A bootstrapped version of the DerSimonian-Laird approach performed best in both detecting heterogeneity and in returning more accurate overall effect estimates. Re-analysing all meta-analyses with this new method we found that in cases where heterogeneity had originally been detected but ignored, 17-20% of the statistical conclusions changed. Rates were much lower where the original analysis did not detect heterogeneity or took it into account, between 1% and 3%.

Conclusions: When evidence for heterogeneity is lacking, standard practice is to assume homogeneity and apply a simpler fixed-effect meta-analysis. We find that assuming homogeneity often results in a misleading analysis, since heterogeneity is very likely present but undetected. Our new method represents a small improvement but the problem largely remains, especially for very small meta-analyses. One solution is to test the sensitivity of the meta-analysis conclusions to assumed moderate and large degrees of heterogeneity. Equally, whenever heterogeneity is detected, it should not be ignored.

Figure 1. All meta-analyses, including single-study and subgroup meta-analyses.

Figure 2. Model selection by number of available studies (and % of random-effects meta-analyses)*.

Figure 3. Comparison of zero between-study variance estimates rates in the Cochrane library data and in simulations, using the DerSimonian-Laird method*.

Figure 4. Distribution of between-study variance estimates by method type (including main and subgroup meta-analyses and truncated to 0.5 for better visualisation).

Figure 5. Cumulative distribution of between-study variance estimates by method type (including main and subgroup meta-analyses and truncated to 5 for better visualisation).