Comparison of meta-analysis versus analysis of variance of individual patient data

Meta-analysis is a method of synthesizing the results of independent studies. We consider the case in which there are multiple treatments and a control, with the goal of estimating the relative effect of each treatment based on continuous outcomes. Even when all data are available, rather than only summary data, it has become common to use meta-analytic estimators of treatment contrasts. Alternatively, we could use a two-way analysis of variance model with no interaction in which one factor is study and one factor is treatment. For the unbalanced case, we obtain the surprising result that the standard meta-analysis estimates of treatment contrasts are identical to the least squares estimators of treatment contrasts in the linear model. Because a meta-analysis of individual patient data can be considerably more costly in terms of data retrieval than a meta-analysis of summary data, this equivalence provides for cost-efficient analysis.