Understanding and testing for heterogeneity across 2 x 2 tables: application to meta-analysis

Area of Science:

• Statistics
• Biostatistics
• Medical Research Methodology

Background:

• Meta-analyses are crucial for synthesizing research findings.
• Assessing study homogeneity is vital for valid meta-analysis interpretation.
• Two key forms of heterogeneity, additive and interactive, can impact results.

Purpose of the Study:

• To introduce and detail the use of Bayes factors for testing heterogeneity in meta-analyses.
• To differentiate between additive and interactive forms of heterogeneity.
• To provide a computational method for calculating Bayes factors to assess these heterogeneities.

Main Methods:

• The study proposes three hierarchical models: one with both additive and interactive heterogeneity, one with only additive heterogeneity, and a null model with no heterogeneity.
• Bayes factors are calculated using a bridge sampling method to compare these models.
• The methodology is applied to two real-world examples to illustrate its practical use.

Main Results:

• The application of Bayes factors successfully identified the presence and type of heterogeneity in the example datasets.
• In one example, both additive and interactive heterogeneity were detected.
• The second example demonstrated the presence of additive heterogeneity only, confirming the model's discriminatory power.

Conclusions:

• Bayes factors provide a robust statistical framework for quantifying additive and interactive heterogeneity in meta-analyses.
• The proposed methods and models offer valuable tools for researchers to rigorously evaluate study homogeneity.
• Accurate assessment of heterogeneity enhances the reliability and interpretability of synthesized research findings.