Confidence intervals for the between-study variance in random effects meta-analysis using generalised Cochran heterogeneity statistics

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and exact, methods are an attractive alternative. Here, methodology is developed to compute exact confidence intervals for the between-study variance using generalised versions of Cochran's heterogeneity statistic. If some between-study is anticipated, but it is unclear how much, then a pragmatic approach is to use the reciprocals of the within-study standard errors as weights when computing the confidence interval.