A statistical method for removing unbalanced trials with multiple covariates in meta-analysis

In meta-analysis literature, there are several checklists describing the procedures necessary to evaluate studies from a qualitative point of view, whereas preliminary quantitative and statistical investigations on the “combinability” of trials have been neglected. Covariate balance is an important prerequisite to conduct meta-analysis. We propose a method to identify unbalanced trials with respect to a set of covariates, in presence of covariate imbalance, namely when the randomized controlled trials generate a meta-sample that cannot satisfy the requisite of randomization/combinability in meta-analysis. The method is able to identify the unbalanced trials, through four stages aimed at achieving combinability. The studies responsible for the imbalance are identified, and then they can be eliminated. The proposed procedure is simple and relies on the combined Anderson-Darling test applied to the Empirical Cumulative Distribution Functions of both experimental and control meta-arms. To illustrate the method in practice, two datasets from well-known meta-analyses in the literature are used.