The usual meta-analysis of a sequence of randomized clinical trials only considers the difference between two treatments and produces a point estimate and a confidence interval for a parameter that measures this difference. The usual parameter is the log)odds ratio( linked to Mantel–Haenszel methodology. Inference is made either under the assumption of homogeneity or in a random effects model that takes account of heterogeneity between trials. This paper has two goals. The first is to present a likelihood based method for the estimation of the parameters in the random effects model, which avoids the use of approximating Normal distributions. The second goal is to extend this method to a bivariate random effects model, in which the effects in both groups are supposed random. In this way inference can be made about the relationship between improvement and baseline effect. The method is demonstrated by a meta-analysis dataset of Collins and Langman.