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, 28 (2), 338-48

A Re-Evaluation of the 'Quantile Approximation Method' for Random Effects Meta-Analysis


A Re-Evaluation of the 'Quantile Approximation Method' for Random Effects Meta-Analysis

Dan Jackson et al. Stat Med.


The quantile approximation method has recently been proposed as a simple method for deriving confidence intervals for the treatment effect in a random effects meta-analysis. Although easily implemented, the quantiles used to construct intervals are derived from a single simulation study. Here it is shown that altering the study parameters, and in particular introducing changes to the distribution of the within-study variances, can have a dramatic impact on the resulting quantiles. This is further illustrated analytically by examining the scenario where all trials are assumed to be the same size. A more cautious approach is therefore suggested, where the conventional standard normal quantile is used in the primary analysis, but where the use of alternative quantiles is also considered in a sensitivity analysis.


Figure 1
Figure 1
Funnel plot showing the trial sizes permitted by three alternative simulation studies.
Figure 2
Figure 2
97.5 per cent quantiles of M from the simulation studies. Triangles show the results for the first scenario, where within-study variances lie in the interval [0.06,0.6]; circles show the results for the second scenario, where the within-study variances lie in the interval [0.0009,0.6]. The corresponding solid curves show the fitted regressions and the other solid curve follows the quantiles from the quantile approximation method. The dashed line shows the standard normal quantile, for comparison.
Figure 3
Figure 3
97.5 per cent quantiles of M assuming that all trials are of the same size.

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    1. DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials. 1986;7:177–188. - PubMed
    1. Biggerstaff BJ, Tweedie RL. Incorporating variability of estimates of heterogeneity in the random effects model in meta-analysis. Statistics in Medicine. 1997;16:753–768. - PubMed
    1. Emerson JD, Hoaglin DC, Mosteller F. Simple robust procedures for combining risk differences in sets of 2 × 2 tables. Statistics in Medicine. 1996;15:1465–1488. - PubMed
    1. Hardy RJ, Thompson SG. A likelihood approach to meta-analysis with random effects. Statistics in Medicine. 1996;15:619–629. - PubMed
    1. Sutton AJ, Abrams KR, Jones DR, Sheldon DR, Song F. Methods for Meta-Analysis in Medical Research. Chichester: Wiley; 2002.

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