Funnel chart:

Funnel charts are scatter plots that display treatment effect estimates from individual studies against a measure of study size. The term “funnel chart” comes from the pattern created by increasing precision in estimating the true treatment effect as sample sizes grow. Smaller studies, which have greater variability, appear more widely scattered at the bottom of the plot, while larger studies cluster more closely toward the top, forming a funnel-like shape.[1]

Q & A Forum

Meta Analysis

Q: How should be a funnel chart in Meta Analysis?

Funnel chart:

Characteristics of a funnel chart in Meta-Analysis:

An ideal funnel chart should be in a pyramid shape and look like an inverted funnel.

Axes:
• Treatment Effect (X-axis): Specifies the estimated effect magnitude (e.g., standardized mean difference, odds ratio).
• The Y-axis (Study Precision) is typically the inverse standard error (1/SE) or the standard error (SE) of the effect size.
• Larger studies (with lower SE) cluster higher on the plot, whereas smaller studies (with greater SE) appear lower.

Ideal Shape (Symmetry in the Absence of Bias):

Study should be evenly scattered around the pooled estimate of the effect when bias is absent.
The graph should resemble an inverted funnel, with larger research (greater accuracy) clustering at the top and smaller studies (lower precision) showing a broader spread at the bottom.

Example:

Figure 1 is the funnel plot of the study Renehan AG, Tyson M, Egger M, et al. [4] which plots the effect estimates against standard error of studies showing the association between body mass index and pre-menopausal breast cancer. This is the representation of ideal funnel chart in a meta-analysis.

Publication Bias:

The plot will be distorted, frequently with a gap on one side, if smaller studies with non-significant results are absent it causes meta-analyses to overestimate treatment effects.

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Methodological Bias:

Treatment effects are often overstated in small, subpar research. Causes asymmetry by favouring greater effect sizes in smaller studies.

Factors affecting symmetry in funnel chart:

Studies or specific results are less likely to be published if they lack statistical significance or if the observed effect size is minimal or absent.
Studies with weaker methodologies may overestimate the effect of an intervention compared to well-designed studies.
A treatment’s significant benefit may only be evident in high-risk patients, who are more frequently included in smaller, early-stage trials. This can result in funnel plot asymmetry.
Standardized mean differences and odds ratios are two examples of effect size estimates that naturally correspond with their standard errors. Even in the absence of bias, this association could produce a deceptive asymmetry in the funnel plot.

Conclusion:

A well-designed meta-analysis funnel chart should have symmetry and resemble an inverted funnel. Any shape asymmetry points to bias, such as heterogeneity, publishing bias, or methodological bias.[2] [3]

References:

https://s4be.cochrane.org/blog/2023/06/27/how-to-read-a-funnel-plot
Sterne JAC, Harbord RM. Funnel plots in meta-analysis. Stata J. 2004;4(2):127-141. https://doi/pdf/10.1177/1536867X0400400204
Anzures-Cabrera J, Higgins JPT. Graphical displays for meta-analysis: An overview with suggestions for practice. J R Stat Soc Ser A Stat Soc. 2010;173(3):569-594. doi:10.1002/jrsm.6.
Renehan AG, Tyson M, Egger M, Heller RF, Zwahlen M. Body-mass index and incidence of cancer: A systematic review and meta-analysis of prospective observational studies. Lancet. 2008;371(9612):569-578. doi:10.1016/S0140-6736(08)60269-X.