This work addresses the issue of partially missing correlations within the framework of bivariate and surrogate meta-analyses. While restricting the analysis to complete-case studies may appear to constitute the most straightforward analytical strategy, such an approach has been demonstrated to yield substantial inefficiencies and potential bias in the resulting estimates. Current methodological contributions in the literature circumvent this limitation either through aggregate estimation procedures grounded in likelihood-based frameworks under simplifying assumptions, or by resorting to deterministic imputation strategies, such as the empirical mean derived from observed units. In the present paper, we propose a multiple imputation framework in which imputation is performed via stochastic procedures based on a Beta regression model, thereby explicitly accounting for the missing at random (MAR) assumption underlying the observed missingness mechanism. We demonstrate the effectiveness of our method through an extensive simulation study across various scenarios, comparing our proposal with simple mean imputation and complete-case analysis under the MAR assumption.

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