Meta-analysis of Observational Studies: a New Balancing Procedure

We propose a new pre-assessment and balancing procedure for multi-treatment meta-analyses of observational studies based on weighted empirical cumulative distribution functions (ECDFs) of a covariate of interest. The method extends existing combinability checks beyond the two-treatment setting by introducing five non-parametric imbalance statistics, designed to capture discrepancies among meta-arms. Statistical significance is assessed through a permutation framework, and imbalance is reduced through an iterative selection procedure that removes study-treatment units, rather than excluding entire studies. A simulation study evaluates the procedure in different scenarios of between-group mean separation and within-group dispersion. Results show that the proportion of removed units increases with distributional divergence and heterogeneity, while the procedure effectively reduces imbalance.