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: plotnine 0.15.5 | Python 3.13.13
Quality: 90/100 | Updated: 2026-06-10
"""
import os
import sys
import numpy as np
import pandas as pd
# Work around naming conflict with plotnine.py script and plotnine package
script_dir = os.path.dirname(os.path.abspath(__file__))
if script_dir in sys.path:
sys.path.remove(script_dir)
if "" in sys.path:
sys.path.remove("")
if "." in sys.path:
sys.path.remove(".")
from plotnine import (
aes,
annotate,
element_blank,
element_line,
element_rect,
element_text,
geom_line,
geom_point,
geom_polygon,
geom_vline,
ggplot,
guide_legend,
guides,
labs,
scale_color_manual,
scale_shape_manual,
scale_size_continuous,
scale_x_continuous,
scale_y_reverse,
theme,
theme_minimal,
)
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — brand green for inside funnel, semantic red for outside/bias
BRAND = "#009E73"
OUTLIER_COLOR = "#AE3030" # matte red — semantic anchor for bad/outlier/bias
# Data — 15 RCTs comparing drug vs placebo (log odds ratios)
np.random.seed(42)
n_studies = 15
true_effect = 0.3
std_errors = np.concatenate(
[np.random.uniform(0.05, 0.15, 5), np.random.uniform(0.15, 0.30, 5), np.random.uniform(0.30, 0.50, 5)]
)
effect_sizes = true_effect + np.random.normal(0, std_errors)
# Add publication bias: shift imprecise (high-SE) studies toward positive
bias_mask = std_errors > 0.35
effect_sizes[bias_mask] += np.random.uniform(0.04, 0.12, bias_mask.sum())
# Clip to keep x-axis balanced and avoid extreme outliers
effect_sizes = np.clip(effect_sizes, -0.55, 0.78)
summary_effect = float(np.average(effect_sizes, weights=1 / std_errors**2))
# Inverse-variance weight for point sizing
weights = 1 / std_errors**2
weight_normalized = weights / weights.max()
# Classify each study by funnel region
lower_ci = summary_effect - 1.96 * std_errors
upper_ci = summary_effect + 1.96 * std_errors
outside_funnel = (effect_sizes < lower_ci) | (effect_sizes > upper_ci)
region = np.where(outside_funnel, "Outside funnel", "Inside funnel")
studies_df = pd.DataFrame(
{
"effect_size": effect_sizes,
"std_error": std_errors,
"weight": weight_normalized,
"region": pd.Categorical(region, categories=["Inside funnel", "Outside funnel"]),
}
)
# Funnel boundary lines (pseudo 95% CI around pooled effect)
se_max = 0.55
se_range = np.linspace(0, se_max, 200)
funnel_lines = pd.DataFrame(
{
"effect": np.concatenate([summary_effect - 1.96 * se_range, summary_effect + 1.96 * se_range]),
"se": np.concatenate([se_range, se_range]),
"side": ["lower"] * len(se_range) + ["upper"] * len(se_range),
}
)
# Funnel polygon for shaded interior region
funnel_poly = pd.DataFrame(
{"x": [summary_effect, summary_effect - 1.96 * se_max, summary_effect + 1.96 * se_max], "y": [0.0, se_max, se_max]}
)
# Title
title = "funnel-meta-analysis · python · plotnine · anyplot.ai"
# Plot
plot = (
ggplot()
+ geom_polygon(funnel_poly, aes(x="x", y="y"), fill=BRAND, alpha=0.08)
+ geom_line(funnel_lines, aes(x="effect", y="se", group="side"), color=INK_SOFT, linetype="dashed", size=0.7)
+ geom_vline(xintercept=summary_effect, color=BRAND, size=1.2)
+ geom_vline(xintercept=0, color=INK_MUTED, linetype="dotted", size=0.7)
+ geom_point(
studies_df,
aes(x="effect_size", y="std_error", size="weight", color="region", shape="region"),
alpha=0.85,
stroke=0.3,
)
+ scale_size_continuous(range=(2.5, 8), guide=None)
+ scale_color_manual(values={"Inside funnel": BRAND, "Outside funnel": OUTLIER_COLOR}, name="")
+ scale_shape_manual(values={"Inside funnel": "o", "Outside funnel": "^"}, name="")
+ guides(color=guide_legend(override_aes={"shape": ["o", "^"]}), shape=False)
+ annotate(
"text",
x=summary_effect + 0.45,
y=0.08,
label="Asymmetry suggests\npublication bias",
size=11,
color=OUTLIER_COLOR,
fontstyle="italic",
ha="center",
)
+ annotate(
"text",
x=summary_effect + 0.02,
y=0.01,
label=f"Pooled effect = {summary_effect:.2f}",
size=10,
color=BRAND,
ha="left",
va="top",
)
+ annotate("text", x=-0.02, y=0.01, label="Null", size=10, color=INK_MUTED, ha="right", va="top")
+ scale_y_reverse(limits=(0.60, -0.02))
+ scale_x_continuous(breaks=np.arange(-0.6, 1.2, 0.2).round(1).tolist())
+ labs(x="Log Odds Ratio", y="Standard Error", color="", title=title)
+ theme_minimal()
+ theme(
figure_size=(8, 4.5),
plot_title=element_text(size=12, weight="bold", color=INK),
axis_title=element_text(size=10, color=INK),
axis_text=element_text(size=8, color=INK_SOFT),
panel_grid_major_y=element_line(color=INK, size=0.3, alpha=0.12),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_background=element_rect(fill=PAGE_BG, color="none"),
plot_background=element_rect(fill=PAGE_BG, color="none"),
legend_position=(0.12, 0.12),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_text=element_text(size=8, color=INK_SOFT),
legend_title=element_blank(),
axis_line=element_line(color=INK_SOFT, size=0.5),
)
)
# Save
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in")
Part of Meta-Analysis Funnel Plot for Publication Bias on anyplot.ai.