1. Egger’s Regression Test

Purpose: Detects publication bias by examining the asymmetry of a funnel plot in meta-analysis.

How it Works:

• A linear regression model is applied to test the association between the standard error (SE) of studies and their effect sizes.
• If small studies tend to show larger effects than large studies, it indicates potential publication bias.

Best Use Cases: ✅ Continuous outcomes (e.g., mean differences, regression coefficients, log odds ratios, log risk ratios).
✅ Works well when ≥10 studies are available.
✅ Easy to implement in software like R, Stata, and RevMan.

Limitations: ❌ Low statistical power when the number of studies is <10.
❌ More sensitive to small-study effects rather than pure publication bias.
❌ Not recommended for binary outcomes (e.g., odds ratios from case-control studies).

 

2. Begg’s Rank Correlation Test

Purpose: A non-parametric test that evaluates whether there is a correlation between effect sizes and their variances to detect publication bias.

How it Works:

• Uses Kendall’s Tau correlation coefficient to test for bias in the distribution of studies within a funnel plot.
• Unlike Egger’s, this method does not assume a linear relationship between effect size and variance.

Best Use Cases: ✅ Can be used for both continuous and binary outcomes (e.g., odds ratios).
✅ Works well for smaller datasets compared to Egger’s test.
✅ Less sensitive to outliers and heterogeneity in studies.

Limitations: ❌ Less powerful than Egger’s test (higher chance of false negatives).
❌ Cannot quantify the degree of bias, only detects its presence.
❌ Works poorly when there are few studies (<10).

 

3. Harbord’s Test

Purpose: Similar to Egger’s test but specifically designed for binary outcomes (odds ratios in case-control and cohort studies).

How it Works:

• Uses a modified linear regression model of log odds ratios against their standard errors.
• Unlike Egger’s test, it adjusts for the variance structure of binary data, making it more robust.

Best Use Cases: ✅ Binary outcomes (e.g., odds ratios, proportions).
✅ More reliable than Egger’s test when dealing with rare events.
✅ Recommended over Egger’s test when meta-analyzing odds ratios (ORs) from case-control studies.

Limitations: ❌ Less effective when study sample sizes are highly imbalanced.
❌ Requires specialized statistical software (available in Stata, but not as widely used in R or RevMan).