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: seaborn 0.13.2 | Python 3.13.13
Quality: 87/100 | Updated: 2026-06-10
"""
import os
import sys
# Remove script directory from sys.path to prevent sibling .py files from
# shadowing installed packages (e.g. matplotlib.py → import matplotlib conflict)
_script_dir = os.path.dirname(os.path.abspath(__file__))
if _script_dir in sys.path:
sys.path.remove(_script_dir)
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib.lines import Line2D
# Theme-adaptive chrome 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 — canonical order, first series always #009E73
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Seaborn theme with theme-adaptive chrome
sns.set_theme(
style="ticks",
rc={
"figure.facecolor": PAGE_BG,
"axes.facecolor": PAGE_BG,
"axes.edgecolor": INK_SOFT,
"axes.labelcolor": INK,
"text.color": INK,
"xtick.color": INK_SOFT,
"ytick.color": INK_SOFT,
"grid.color": INK_SOFT,
"grid.alpha": 0.2,
"grid.linewidth": 0.6,
"axes.grid": False,
"legend.facecolor": ELEVATED_BG,
"legend.edgecolor": INK_SOFT,
"font.family": "sans-serif",
},
)
sns.set_context("notebook", font_scale=1.0)
# Data
np.random.seed(42)
studies = [
"Adams 2018",
"Baker 2019",
"Chen 2017",
"Diaz 2020",
"Evans 2016",
"Fischer 2021",
"Garcia 2019",
"Hughes 2018",
"Ibrahim 2020",
"Jones 2017",
"Kim 2021",
"Lee 2019",
"Martinez 2020",
"Novak 2018",
"O'Brien 2022",
]
n_studies = len(studies)
true_effect = -0.35
std_errors = np.concatenate(
[np.random.uniform(0.05, 0.15, 5), np.random.uniform(0.15, 0.30, 6), np.random.uniform(0.30, 0.50, 4)]
)
effect_sizes = true_effect + np.random.normal(0, 1, n_studies) * std_errors
effect_sizes[-2] += 0.25
effect_sizes[-1] += 0.30
weights = 1 / std_errors**2
summary_effect = np.average(effect_sizes, weights=weights)
df = pd.DataFrame({"effect_size": effect_sizes, "std_error": std_errors, "study": studies, "weight": weights})
df["precision"] = pd.cut(
df["std_error"], bins=[0, 0.15, 0.30, 1.0], labels=["High precision", "Moderate precision", "Low precision"]
)
# Plot — landscape 3200×1800 px (hard rule: figsize=(8, 4.5), dpi=400, no bbox_inches='tight')
fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400)
se_range = np.linspace(0, 0.55, 300)
ci_left = summary_effect - 1.96 * se_range
ci_right = summary_effect + 1.96 * se_range
# Pseudo 95% CI funnel region
ax.fill_betweenx(se_range, ci_left, ci_right, color=INK_MUTED, alpha=0.10)
ax.plot(ci_left, se_range, color=INK_SOFT, linewidth=1.2, linestyle="--", alpha=0.5)
ax.plot(ci_right, se_range, color=INK_SOFT, linewidth=1.2, linestyle="--", alpha=0.5)
# Reference lines: summary effect (structural INK neutral) and null effect
ax.axvline(x=summary_effect, color=INK, linewidth=2.0, alpha=0.85, zorder=4)
ax.axvline(x=0, color=INK_SOFT, linewidth=1.2, linestyle=":", alpha=0.5, zorder=3)
# Scatter by precision tier — Imprint palette; high precision → green (semantic: quality/good)
tier_palette = {
"High precision": IMPRINT_PALETTE[0],
"Moderate precision": IMPRINT_PALETTE[1],
"Low precision": IMPRINT_PALETTE[2],
}
sns.scatterplot(
data=df,
x="effect_size",
y="std_error",
hue="precision",
size="weight",
sizes=(60, 280),
palette=tier_palette,
edgecolor="white",
linewidth=0.8,
alpha=0.85,
zorder=5,
ax=ax,
legend=False,
)
# Seaborn rugplot for marginal effect size distribution — idiomatic seaborn feature
sns.rugplot(data=df, x="effect_size", height=0.04, color=INK_SOFT, alpha=0.65, ax=ax)
# Annotate two most imprecise (lower-right outlier) studies
# Martinez 2020 is rightmost — use left-aligned offset to avoid right canvas edge
outliers = df.nlargest(2, "std_error")
for _, row in outliers.iterrows():
x_offset = -75 if row["study"] == "Martinez 2020" else 10
ax.annotate(
row["study"],
xy=(row["effect_size"], row["std_error"]),
xytext=(x_offset, -3),
textcoords="offset points",
fontsize=8,
fontstyle="italic",
color=INK_MUTED,
)
# Axis style
ax.invert_yaxis()
ax.set_xlabel("Log Odds Ratio (Drug vs Placebo)", fontsize=10)
ax.set_ylabel("Standard Error", fontsize=10)
ax.set_title(
"funnel-meta-analysis · python · seaborn · anyplot.ai", fontsize=12, fontweight="medium", pad=10, color=INK
)
ax.tick_params(axis="both", labelsize=8)
# X-axis: asymmetric limits covering the full funnel extent at max SE plus data range
x_min = min(summary_effect - 1.96 * 0.55, df["effect_size"].min()) - 0.08
x_max = max(summary_effect + 1.96 * 0.55, df["effect_size"].max()) + 0.08
ax.set_xlim(x_min, x_max)
sns.despine(ax=ax)
# Y-axis-only grid (style guide preference)
ax.yaxis.grid(True, alpha=0.2, linewidth=0.8, color=INK_SOFT)
ax.xaxis.grid(False)
# Legend
legend_elements = [
Line2D([0], [0], color=INK, linewidth=2.0, alpha=0.85, label=f"Summary effect ({summary_effect:.2f})"),
Line2D([0], [0], color=INK_SOFT, linewidth=1.2, linestyle=":", alpha=0.5, label="Null effect (0)"),
Line2D([0], [0], marker="o", color="w", markerfacecolor=IMPRINT_PALETTE[0], markersize=7, label="High precision"),
Line2D(
[0], [0], marker="o", color="w", markerfacecolor=IMPRINT_PALETTE[1], markersize=6, label="Moderate precision"
),
Line2D([0], [0], marker="o", color="w", markerfacecolor=IMPRINT_PALETTE[2], markersize=5, label="Low precision"),
]
ax.legend(handles=legend_elements, fontsize=8, frameon=False, loc="lower left")
# Size encoding note and weighted-mean apex label for information density
ax.text(
0.98,
0.03,
"Circle size ∝ study weight",
transform=ax.transAxes,
ha="right",
va="bottom",
fontsize=7,
color=INK_MUTED,
fontstyle="italic",
)
ax.annotate(
f"WM = {summary_effect:.2f}",
xy=(summary_effect, 0.01),
xytext=(summary_effect + 0.12, 0.06),
fontsize=7,
color=INK_SOFT,
arrowprops={"arrowstyle": "-", "color": INK_MUTED, "lw": 0.7},
)
# Save — no bbox_inches; figsize×dpi produces exact 3200×1800 target
# Use __file__-relative path so script runs correctly from any working directory
output_dir = os.path.dirname(os.path.abspath(__file__))
plt.savefig(os.path.join(output_dir, f"plot-{THEME}.png"), dpi=400, facecolor=PAGE_BG)
plt.close()
Part of Meta-Analysis Funnel Plot for Publication Bias on anyplot.ai.