Neither fixed nor random: weighted least squares meta-regression.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Conventional meta-regression estimators, including mixed-effects and fixed-effects meta-regression analysis (FE-MRA), are widely used.
• These methods may be susceptible to biases, particularly publication bias or small-sample bias.

Purpose of the Study:

• To challenge and revisit the conventional meta-regression estimators.
• To introduce and validate an unrestricted weighted least squares meta-regression analysis (WLS-MRA) estimator.
• To compare the performance of WLS-MRA against traditional methods under various conditions, including the presence of publication bias.

Main Methods:

• The study employed statistical theory and simulation analyses.
• Meta-regression analyses were conducted using conventional mixed-effects, random-effects, and fixed-effects meta-regression analysis (FE-MRA) estimators.
• An unrestricted weighted least squares meta-regression analysis (WLS-MRA) estimator was developed and applied.

Main Results:

• WLS-MRA demonstrates superior performance compared to conventional random-effects meta-regression when publication bias is present.
• In the absence of publication bias, WLS-MRA provides estimates practically equivalent to mixed-effects or random-effects models.
• When publication selection bias exists, WLS-MRA consistently yields estimates with smaller bias than mixed-effects or random-effects approaches.

Conclusions:

• Unrestricted WLS meta-regression is a robust and often superior alternative to traditional meta-regression techniques, especially when publication bias is a concern.
• While WLS-MRA is generally recommended, random-effects meta-regression may still be preferable if publication bias is absent and specific heterogeneity conditions are met.