A funnel plot used in meta-analysis to assess publication bias by plotting individual study effect sizes against their precision (typically standard error). Studies scatter around a summary effect line, with pseudo 95% confidence limits forming an inverted funnel shape. In the absence of bias, studies distribute symmetrically around the summary effect; asymmetry suggests publication bias or systematic heterogeneity. This is a standard tool in systematic reviews and Cochrane-style meta-analyses.
# anyplot.ai
# funnel-meta-analysis: Meta-Analysis Funnel Plot for Publication Bias
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 91/100 | Created: 2026-06-10
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73", # 1 — brand green (first series)
colorant"#C475FD", # 2 — lavender
colorant"#4467A3", # 3 — blue
colorant"#BD8233", # 4 — ochre
colorant"#AE3030", # 5 — matte red
colorant"#2ABCCD", # 6 — cyan
colorant"#954477", # 7 — rose
colorant"#99B314", # 8 — lime
]
# Data: 20 RCTs on antihypertensive drug vs placebo (log odds ratio of major CV events)
const summary_effect = -0.38
std_errors = [0.07, 0.09, 0.11, 0.12, 0.14, 0.16, 0.18, 0.20, 0.23, 0.25,
0.28, 0.31, 0.33, 0.36, 0.38, 0.41, 0.44, 0.47, 0.50, 0.54]
n_studies = length(std_errors)
# Slight small-study asymmetry: smaller trials claim larger benefit (publication bias)
small_study_bias = -0.25 .* (std_errors ./ maximum(std_errors))
effect_sizes = summary_effect .+ small_study_bias .+ randn(n_studies) .* std_errors
# Funnel 95% confidence limit boundary
max_se_plot = maximum(std_errors) * 1.12
n_pts = 200
se_grid = collect(range(0.0, max_se_plot; length=n_pts))
funnel_lo = summary_effect .- 1.96 .* se_grid
funnel_hi = summary_effect .+ 1.96 .* se_grid
# Funnel fill polygon (trace lo top→bottom, then hi bottom→top)
funnel_polygon = [
[Point2f(funnel_lo[i], se_grid[i]) for i in 1:n_pts];
[Point2f(funnel_hi[i], se_grid[i]) for i in n_pts:-1:1]
]
# Plot
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(fig[1, 1];
title = "funnel-meta-analysis · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Log Odds Ratio",
ylabel = "Standard Error",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridvisible = false,
ygridvisible = false,
yreversed = true,
)
# Funnel shaded region
poly!(ax, funnel_polygon;
color = RGBAf(INK_MUTED.r, INK_MUTED.g, INK_MUTED.b, 0.12),
strokewidth = 0)
# 95% CI boundary lines
lines!(ax, funnel_lo, se_grid; color = INK_SOFT, linewidth = 1.5, linestyle = :dash)
lines!(ax, funnel_hi, se_grid; color = INK_SOFT, linewidth = 1.5, linestyle = :dash)
# Null effect reference line (log OR = 0 ↔ OR = 1)
vlines!(ax, [0.0]; color = INK_MUTED, linewidth = 1.5, linestyle = :dot)
# Pooled effect line
vlines!(ax, [summary_effect]; color = IMPRINT_PALETTE[3], linewidth = 2.0)
# Individual study points
scatter!(ax, effect_sizes, std_errors;
color = IMPRINT_PALETTE[1],
markersize = 14,
strokewidth = 1.0,
strokecolor = PAGE_BG)
# Annotation: small-study asymmetry signals potential publication bias
text!(ax, funnel_hi[end] - 0.05, max_se_plot * 0.92;
text = "← Asymmetric scatter:\npossible publication bias",
align = (:right, :center),
fontsize = 11,
color = INK_MUTED,
font = :italic)
# Axis limits
ylims!(ax, (0.0, max_se_plot))
xlims!(ax, (funnel_lo[end] - 0.08, funnel_hi[end] + 0.08))
# Legend
elem_studies = MarkerElement(marker = :circle, color = IMPRINT_PALETTE[1],
strokecolor = PAGE_BG, strokewidth = 1.0, markersize = 14)
elem_pooled = LineElement(color = IMPRINT_PALETTE[3], linewidth = 2.0)
elem_null = LineElement(color = INK_MUTED, linewidth = 1.5, linestyle = :dot)
elem_ci = LineElement(color = INK_SOFT, linewidth = 1.5, linestyle = :dash)
Legend(fig[1, 2],
[elem_studies, elem_pooled, elem_null, elem_ci],
["Individual study (n=20)",
"Pooled effect (OR = $(round(exp(summary_effect), digits=2)))",
"Null effect (OR = 1.0)",
"95% confidence limits"],
framevisible = true,
framecolor = INK_SOFT,
backgroundcolor = ELEVATED_BG,
labelsize = 13,
padding = (12, 12, 10, 10),
rowgap = 6,
)
colsize!(fig.layout, 1, Relative(0.80))
# Save
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/funnel-meta-analysis/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "funnel-meta-analysis",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/funnel-meta-analysis/julia/makie",
"hub": "https://anyplot.ai/funnel-meta-analysis",
"code_json": "https://api.anyplot.ai/specs/funnel-meta-analysis/makie/code",
"spec_json": "https://api.anyplot.ai/specs/funnel-meta-analysis",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/funnel-meta-analysis/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/funnel-meta-analysis/julia/makie/plot-dark.png",
"quality_score": 91.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Meta-Analysis Funnel Plot for Publication Bias on anyplot.ai.