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The random effects approach in meta-analysis due to DerSimonian and Laird is well established and used pervasively. It has been established by Brockwell and Gordon that this method, when used for confidence intervals, leads to coverage probabilities lower than the nominal value. A number of alternatives have been proposed, but these either have the defect of iterative and complicated calculation, or deficient coverage. In this paper we propose a new approach, which is simple to use, and has coverage probabilities better than the alternatives, based on extensive simulation. We call this approach the 'quantile approximation' method., (Copyright 2007 John Wiley & Sons, Ltd.)

Meta-analysis may be used to estimate an overall effect across a number of similar studies. A number of statistical techniques are currently used to combine individual study results. The simplest of these is based on a fixed effects model, which assumes the true effect is the same for all studies. A random effects model, however, allows the true effect to vary across studies, with the mean true effect the parameter of interest. We consider three methods currently used for estimation within the framework of a random effects model, and illustrate them by applying each method to a collection of six studies on the effect of aspirin after myocardial infarction. These methods are compared using estimated coverage probabilities of confidence intervals for the overall effect. The techniques considered all generally have coverages below the nominal level, and in particular it is shown that the commonly used DerSimonian and Laird method does not adequately reflect the error associated with parameter estimation, especially when the number of studies is small., (Copyright 2001 John Wiley & Sons, Ltd.)