Speakers
Abstract
The classical meta-analytical random-effects model (REM), when applied to the standardized mean difference, $g$, is usually computed by taking the conditional (to the parameter) variance of $g$, instead of the unconditional variance, to estimate the sampling variance in the specific studies involved. This practice introduces dependencies between the effect size (ES) estimates and their variances, which can distort estimation procedures. Additionally, the traditional handling of $g$'s variance in REM leads to biased estimates, as the positive relationship between $g$ and its conditional variance results in underestimation of $\mu_{\Delta}$.
To address these issues, Suero et al. (2025) developed a random-effects model reformulated as a mixture model (MM). This framework is a flexible alternative that encompasses ES indices in which the estimate and its estimated variance are stochastically dependent, and ES indices in which they are independent. It also yields new estimators of the variance of true effects, or specific variance $\tau^2$, and of the mean effect $\mu_{\Delta}$. Nevertheless, deriving an estimator for the variance of $\hat{\tau}^2$ and characterizing its distribution remained outstanding tasks.
In this study, we derive an analytical expression for the parametric variance of the $\tau^2$ estimator under the MM approach, which is crucial for assessing estimation precision. To achieve this, we rely on fundamental theorems from mathematical analysis, key algebraic results, and essential properties of estimators, ensuring a rigorous derivation. An extensive simulation study is conducted to assess the accuracy of the variance formula. This constitutes a step toward understanding the distribution of the estimator, which in turn will allow us to construct a confidence interval.
| Poster | Beyond Classical Random Effects Meta-Analysis: Parametric Variance of the Specific Variance Estimator Under a Mixture Model Framework for Standardized Mean Difference |
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| Author | Alba Lirón León |
| Affiliation | Universidad Autónoma de Madrid |
| Keywords | meta-analysis, mixture random effects model |
