Grey Relational Meta-Analysis: a robust pooling method with a redescending effect guard

Abstract

Background. Inverse-variance meta-analysis can be sensitive to extreme effect outliers and high-leverage studies. Existing robust alternatives (M-estimators, heavy-tailed likelihoods, mixture models) address this, but a practical niche remains for methods that combine effect and precision information transparently with nonparametric inference.

Methods. We propose Grey Relational Meta-Analysis (GRMA), a robust pooling estimator that uses grey relational similarity in a two-feature space (effect size and log-precision) with an explicit Tukey bisquare effect guard and bootstrap percentile-interval inference. We evaluated GRMA by simulation (2,000 replicates, 25 scenarios, 4 comparators: restricted maximum likelihood [REML], Hartung–Knapp–Sidik–Jonkman [HKSJ], weighted robust dispersion [WRD] and robust Bayesian mixture [RBM]) and on 4,572 real Cochrane meta-analyses (the Pairwise70 benchmark).

Results. In simulation, GRMA reduced absolute bias in 4 of 5 outlier scenarios (up to 66% reduction), with root-mean-squared error (RMSE) comparable to HKSJ in outlier scenarios (ratio 1.01) but 8–18% higher under uncontaminated conditions; power was correspondingly lower under standard conditions (59% versus 72% at k = 10, τ² = 0.05). Bootstrap percentile intervals achieved mean coverage of 0.940 (excluding publication-bias stress tests, where all methods suffer). In the Pairwise70 benchmark (4,572 Cochrane meta-analyses) GRMA estimates correlated r = 0.956 with random-effects estimates, increasing to r = 0.980 at k ≥ 10.

Conclusions. GRMA is a transparent robust pooling method, proposed as a companion to standard random-effects models rather than a replacement. All code (R and Python) and data are provided in a reproducible capsule under an MIT licence.