Abstract
BackgroundThe DerSimonian and Laird approach (DL) is widely used for random effects meta-analysis, but this often results in inappropriate type I error rates. The method described by Hartung, Knapp, Sidik and Jonkman (HKSJ) is known to perform better when trials of similar size are combined. However evidence in realistic situations, where one trial might be much larger than the other trials, is lacking. We aimed to evaluate the relative performance of the DL and HKSJ methods when studies of different sizes are combined and to develop a simple method to convert DL results to HKSJ results.MethodsWe evaluated the performance of the HKSJ versus DL approach in simulated meta-analyses of 2–20 trials with varying sample sizes and between-study heterogeneity, and allowing trials to have various sizes, e.g. 25% of the trials being 10-times larger than the smaller trials. We also compared the number of “positive” (statistically significant at p < 0.05) findings using empirical data of recent meta-analyses with > = 3 studies of interventions from the Cochrane Database of Systematic Reviews.ResultsThe simulations showed that the HKSJ method consistently resulted in more adequate error rates than the DL method. When the significance level was 5%, the HKSJ error rates at most doubled, whereas for DL they could be over 30%. DL, and, far less so, HKSJ had more inflated error rates when the combined studies had unequal sizes and between-study heterogeneity. The empirical data from 689 meta-analyses showed that 25.1% of the significant findings for the DL method were non-significant with the HKSJ method. DL results can be easily converted into HKSJ results.ConclusionsOur simulations showed that the HKSJ method consistently results in more adequate error rates than the DL method, especially when the number of studies is small, and can easily be applied routinely in meta-analyses. Even with the HKSJ method, extra caution is needed when there are = <5 studies of very unequal sizes.
Highlights
The DerSimonian and Laird approach (DL) is widely used for random effects meta-analysis, but this often results in inappropriate type I error rates
The lines connect the means of these error rates
DL error rates for meta-analyses of five studies ranged between 5.7% for sized trials and 14.7% for mixtures of trial sizes (Table 1)
Summary
The DerSimonian and Laird approach (DL) is widely used for random effects meta-analysis, but this often results in inappropriate type I error rates. For the DL method, the error rate can be substantially higher, unless the number of studies is large (≫ 20) and there is no or only minimal heterogeneity [4,5,6,7,8,9,10] Given this deficiency, alternative methods for random effects meta-analysis have been proposed. Simulations have shown that the HKSJ method performs better than DL, especially when there is heterogeneity and the number of studies in the meta-analysis is small [4,5,6,7,8,9,10,11,12,13,14]. Some detectable heterogeneity is present in about half of meta-analyses of clinical studies [15,16,17,18]
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