A REML method for the evidence-splitting model in network meta-analysis

Checking for possible inconsistency between direct and indirect evidence is an important task in network meta-analysis. Recently, an evidence-splitting (ES) model has been proposed, that allows separating direct and indirect evidence in a network and hence assessing inconsistency. A salient feature of this model is that the variance for heterogeneity appears in both the mean and the variance structure. Thus, full maximum likelihood (ML) has been proposed for estimating the parameters of this model. Maximum likelihood is known to yield biased variance component estimates in linear mixed models, and this problem is expected to also affect the ES model. The purpose of the present paper, therefore, is to propose a method based on residual (or restricted) maximum likelihood (REML). Our simulation shows that this new method is quite competitive to methods based on full ML in terms of bias and mean squared error. In addition, some limitations of the ES model are discussed. While this model splits direct and indirect evidence, it is not a plausible model for the cause of inconsistency.