Trim-and-fill funnel plot

Funnel plot with imputed studies

A funnel plot with algorithmically imputed “missing” studies that would make it symmetric, and the adjusted pooled estimate.

MAEstablished

Trim-and-fill funnel plot of the passive smoking studies. Filled circles are observed studies; open circles are the seven studies imputed on the left to restore symmetry. The vertical line is the adjusted pooled estimate. Data: metadat::dat.hackshaw1998.

Family

Small-study effects and reporting bias

Purpose

Provide a sensitivity analysis for funnel asymmetry by imputing mirror-image studies.

Inputs

Study estimates with standard errors.

Software

R metafor::trimfill(), meta::trimfill(); Stata meta trimfill

What it shows

Duval and Tweedie’s trim-and-fill method estimates how many studies are missing from the sparse side of the funnel, “trims” the most extreme studies from the other side, re-estimates the center, and then “fills” in mirror images of the trimmed studies. The plot shows the observed studies, the imputed ones in a different symbol, and the adjusted pooled estimate.

How to read it

Filled points: observed studies.
Open points: imputed studies, mirror images of observed ones.
Vertical line: the pooled estimate after filling.
Funnel: pseudo-confidence limits around the adjusted estimate.

Interpretation

Seven studies are imputed on the left. The pooled odds ratio falls from 1.24 to 1.19 (95% CI 1.08 to 1.31), so the association persists under this adjustment. A reasonable conclusion is that the result is fairly robust to the kind of asymmetry trim-and-fill assumes, not that the true effect is 1.19.

Pitfalls

Imputed studies are not real missing studies; they are an artifact of the symmetry assumption.
The adjusted estimate is not a bias-corrected truth. The method performs poorly when heterogeneity is large and when asymmetry has causes other than publication bias.
Results depend on the estimator of the number of missing studies (\(L_0\) or \(R_0\)) and on the model.

Code

library(metafor)

data(dat.hackshaw1998, package = "metadat")

fit <- rma(yi, vi, data = dat.hackshaw1998, method = "REML")

# Trim-and-fill imputes "missing" studies to make the funnel symmetric
tf <- trimfill(fit)

funnel(tf, atransf = exp, at = log(c(0.25, 0.5, 1, 2, 4, 8)),
       pch = 21, bg = "#9fb3c8", col = "#1d4e89",
       pch.fill = 21, col.fill = "#b5452b",
       legend = list(show = "cis"),
       xlab = "Odds ratio (log scale)")

meta set yi sei
meta trimfill, funnel

References

Duval S, Tweedie R. Trim and fill: a simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis. Biometrics. 2000;56:455-463. doi:10.1111/j.0006-341X.2000.00455.x
Peters JL, Sutton AJ, Jones DR, Abrams KR, Rushton L. Performance of the trim and fill method in the presence of publication bias and between-study heterogeneity. Stat Med. 2007;26:4544-4562. doi:10.1002/sim.2889