In a meta-analysis of a set of clinical trials, a crucial but problematic component is providing an estimate and confidence interval for the overall treatment effect θ. Since in the presence of heterogeneity a fixed effect approach yields an artificially narrow confidence interval for θ, the random effects method of DerSimonian and Laird, which incorporates a moment estimator of the between-trial components of variance σ2B, has been advocated. With the additional distributional assumptions of normality, a confidence interval for θ may be obtained. However, this method does not provide a confidence interval for σ2B, nor a confidence interval for θ which takes account of the fact that σ2B has to be estimated from the data. We show how a likelihood based method can be used to overcome these problems, and use profile likelihoods to construct likelihood based confidence intervals. This approach yields an appropriately widened confidence interval compared with the standard random effects method. Examples of application to a published meta-analysis and a multicentre clinical trial are discussed. It is concluded that likelihood based methods are preferred to the standard method in undertaking random effects meta-analysis when the value of σ2B has an important effect on the overall estimated treatment effect.