Use funnel plots for an initial visual check of bias. If you seek a formal statistical test, follow up with Egger's test for larger meta-analyses. For smaller samples, consider Begg’s test if Egger's indicates bias, as it may be more robust. If bias is suggested, apply methods like trim-and-fill to adjust for potential publication bias (PB). Combine these with sensitivity analyses to assess the robustness of your results. No method is perfect, but using both visual (Funnel plot) and statistical (Egger’s or Begg’s) approaches provides a comprehensive assessment.

Publication bias can be assessed through both qualitative and quantitative methods. One common qualitative approach is the inverted funnel plot. This method allows you to visually inspect the distribution of studies. Ideally, studies should be symmetrically distributed around the mean effect size. If asymmetry is detected, it may indicate potential publication bias. However, for a reliable assessment of symmetry, it is generally recommended to have at least 10 studies in your meta-analysis. Fewer studies may result in misleading conclusions due to the limited data available for evaluating funnel plot symmetry.

Quantitative tests are often employed to confirm the findings from the funnel plot analysis. Two commonly used statistical tests for this purpose are Egger’s test and Begg’s test. Egger’s test helps detect small-study effects, which may signal publication bias. It is particularly useful when you suspect that smaller studies are systematically overrepresented in the analysis. On the other hand, Begg’s test is recommended when dealing with smaller sample sizes. It is less sensitive to heterogeneity and provides a robust method for identifying publication bias in situations where the number of studies is limited.

If you identify potential publication bias, there are several approaches to mitigate its impact on your results. One method is to add contour-enhanced lines to the funnel plot. This can help identify regions where missing studies might be influencing the analysis. The addition of these contour lines helps visualize the potential impact of publication bias on the results and shows where the "missing" studies could explain the asymmetry. Another approach is the trim and fill method, which estimates the number of missing studies and predicts where they might fall on the funnel plot. This method also provides an adjusted effect size by taking into account the potential missing studies and assessing the statistical significance of the findings.

Both of these methods can be valuable in correcting for publication bias once it has been detected. However, to further validate your findings and account for the sources of potential bias, consider conducting additional analyses, such as sensitivity analysis, leave-one-out analysis, subgroup analysis, and meta-regression analysis. Sensitivity analysis assesses the robustness of your results by examining how they change when individual studies are removed from the analysis. Leave-one-out analysis is similar, systematically removing one study at a time to determine its influence on the overall results. Subgroup analysis helps explore whether the effect size differs across various subgroups, while meta-regression examines the relationship between study characteristics (e.g., sample size, study quality, intervention type) and the effect size. These additional analyses can help strengthen your conclusions and reduce the risk of publication bias affecting your meta-analysis results.

Hope this may helps

I echo the answer above that "No method is perfect, but using both visual (Funnel plot) and statistical (Egger’s or Begg’s) approaches ....." - all comes down to how many studies you have.

The funnel plot is a visual tool that helps identify the possibility of publication bias by displaying the symmetry of effect sizes relative to their standard errors. However, it does not confirm bias; asymmetry could also arise from heterogeneity or other factors. Statistical methods like Egger’s test quantitatively assess small-study effects, while the trim-and-fill method estimates and adjusts for missing studies. For meta-analyses with at least 10 studies, combining these approaches provides a more comprehensive assessment of publication bias, as no single method is definitive ^^

Thanks to all colleagues who responded to my question .. If I would to do subgroup comparison through the meta-analysis, is there any application that is available free to do it.. I tried MedCalc, but it did not apparently include an option to compare between subgroups.

You are most welcome!

R Studio can perform subgroup meta-analyses using the "meta" package, but it requires some coding experience. I can assist with it if needed.

Thanks you Hassan so much for your kind offer.. I have managed to do it using a software called CMA.