Meta-analysis is a powerful method to combine the treatment effects of multiple independent studies answering a common research question. To determine a causal treatment effect in a meta-analysis it is important to look at the characteristics of the participants, like age or diseases, also known as covariates. In the case of experimental studies, participants are randomly allocated to treatment groups. As a result, the covariate is in expectation equally distributed between the treatment groups. In observational studies, no randomisation has occurred and thus, the covariate imbalance between treatment groups may be more profound. This makes it difficult to determine a causal effect of the treatment, since the covariate may affect the outcome. Therefore, it is important to balance these covariates between the treatment, especially for observational studies. The condition when this balance is present is called combinability.

In this thesis, the covariate imbalance between treatment groups is assessed using five multi-sample test statistics. These assessment methods are based on the comparison of the empirical cumulative distribution functions of the covariate between the meta-arms, which are the collections of the similar treatment groups. Then, a permutation test is used to determine whether the covariate imbalance is significant, as assessed by the multi-sample test statistics. This is done by computing a distribution of the multi-sample test statistics under the null hypothesis that there is no covariate imbalance between the meta-arms. If the observed multi-sample test statistics are significantly large, then combinability is not satisfied.

Subsequently, a balancing procedure is proposed to minimise the covariate imbalance if combinability is not satisfied. This balancing procedure works by discarding a selection of treatment groups from the meta-analysis, such that the multi-sample test statistics indicate that the covariate imbalance is no longer significant. The result is a more combinable set of treatment groups that can be used for the purposes of meta-analysis. Finally, a simulation study of the balancing procedure is done for three and four treatment groups. In these simulations, the treatment groups are simulated with different underlying distributions, such that in theory the covariate imbalance is significant. These simulations seem to indicate that the more treatment groups there are, the more groups need to be discarded before the covariate imbalance is no longer significant. This is explained by the fact that the initial covariate imbalance is larger if there are more treatment groups. On average, in the case of three treatment groups, nearly a fifth of groups needs to discarded, while in in the case of four treatment groups, roughly a third of groups needs to be discarded. Finally the use of five multi-sample test statistics in the balancing procedure result in a sizeable overlap of groups that are discarded.