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: pygal 3.1.0 | Python 3.13.13
Quality: 88/100 | Updated: 2026-06-10
"""
import os
import numpy as np
import pygal
from pygal.style import Style
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
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 — first categorical series always #009E73
IMPRINT_GREEN = "#009E73" # position 1 — high-precision studies
IMPRINT_LAVENDER = "#C475FD" # position 2 — low-precision studies
# Data: 15 RCTs comparing drug vs placebo (log odds ratios)
np.random.seed(42)
study_names = [
"Adams 2018",
"Baker 2019",
"Chen 2019",
"Davis 2020",
"Evans 2020",
"Foster 2021",
"Garcia 2021",
"Harris 2022",
"Ibrahim 2022",
"Jones 2022",
"Kim 2023",
"Lee 2023",
"Martinez 2023",
"Nelson 2024",
"O'Brien 2024",
]
# Effect sizes (log odds ratios) and standard errors
# High-precision studies cluster near pooled effect; low-precision studies
# show rightward asymmetry (missing negative small studies = publication bias)
effect_sizes = np.array(
[-0.50, -0.42, -0.68, -0.46, -0.25, -0.55, -0.48, -0.44, -0.38, -0.20, -0.72, -0.43, -0.08, -0.51, -0.58]
)
std_errors = np.array([0.08, 0.11, 0.17, 0.09, 0.16, 0.21, 0.13, 0.07, 0.22, 0.18, 0.26, 0.10, 0.23, 0.12, 0.24])
pooled_effect = -0.47
high_precision_mask = std_errors < 0.15
low_precision_mask = ~high_precision_mask
# Style — theme-adaptive chrome + Imprint palette
# Structural reference lines (CI, pooled effect, null) use INK tokens;
# data series (study groups) use Imprint categorical positions 1 and 3.
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=(
INK_MUTED, # 0: CI left boundary (structural line, not a data category)
INK_MUTED, # 1: CI right boundary (hidden from legend)
INK, # 2: Pooled effect line (structural reference)
INK_SOFT, # 3: Null effect line (structural reference)
IMPRINT_GREEN, # 4: High-precision studies — Imprint position 1
IMPRINT_LAVENDER, # 5: Low-precision studies — Imprint position 2
),
title_font_size=66,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
stroke_width=2.5,
font_family="Helvetica, Arial, sans-serif",
opacity=".9",
opacity_hover="1",
)
# Chart — 3200×1800 landscape canvas
chart = pygal.XY(
width=3200,
height=1800,
explicit_size=True,
title="funnel-meta-analysis · python · pygal · anyplot.ai",
x_title="Log Odds Ratio (Effect Size)",
y_title="Standard Error (precision ↑)",
style=custom_style,
show_legend=True,
legend_at_bottom=True,
legend_at_bottom_columns=2,
legend_box_size=30,
dots_size=14,
stroke=False,
show_y_guides=True,
show_x_guides=False,
margin=120,
inverse_y_axis=True,
truncate_legend=-1,
x_value_formatter=lambda x: f"{x:.2f}",
y_value_formatter=lambda y: f"{y:.2f}",
y_labels=[0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30],
print_values=False,
print_zeroes=False,
range=(0, 0.30),
xrange=(-1.05, 0.15),
spacing=30,
tooltip_border_radius=8,
)
# Funnel boundaries — pseudo 95% CI diagonal lines
se_values = np.linspace(0, 0.30, 60)
funnel_left = [(float(pooled_effect - 1.96 * se), float(se)) for se in se_values]
chart.add(
"95% Pseudo CI",
funnel_left,
stroke=True,
show_dots=False,
stroke_style={"width": 4, "dasharray": "14, 6"},
formatter=lambda x: "",
)
funnel_right = [(float(pooled_effect + 1.96 * se), float(se)) for se in se_values]
chart.add(
None,
funnel_right,
stroke=True,
show_dots=False,
stroke_style={"width": 4, "dasharray": "14, 6"},
formatter=lambda x: "",
)
# Vertical line at pooled effect (solid, prominent)
chart.add(
f"Pooled Effect (LOR = {pooled_effect:.2f})",
[(float(pooled_effect), 0.0), (float(pooled_effect), 0.30)],
stroke=True,
show_dots=False,
stroke_style={"width": 6},
formatter=lambda x: "",
)
# Vertical dashed line at null effect
chart.add(
"Null Effect (LOR = 0)",
[(0.0, 0.0), (0.0, 0.30)],
stroke=True,
show_dots=False,
stroke_style={"width": 3, "dasharray": "10, 8"},
formatter=lambda x: "",
)
# High-precision studies — larger markers, tightly clustered near pooled effect
hp_points = [
{"value": (float(es), float(se)), "label": f"{name}: LOR={es:.2f}, SE={se:.2f}"}
for name, es, se in zip(
np.array(study_names)[high_precision_mask],
effect_sizes[high_precision_mask],
std_errors[high_precision_mask],
strict=True,
)
]
chart.add("High-precision studies", hp_points, stroke=False, dots_size=24, formatter=lambda x: "")
# Low-precision studies — smaller markers, rightward asymmetry signals publication bias
lp_points = [
{"value": (float(es), float(se)), "label": f"{name}: LOR={es:.2f}, SE={se:.2f}"}
for name, es, se in zip(
np.array(study_names)[low_precision_mask],
effect_sizes[low_precision_mask],
std_errors[low_precision_mask],
strict=True,
)
]
chart.add("Low-precision studies (bias region)", lp_points, stroke=False, dots_size=18, formatter=lambda x: "")
# Save
chart.render_to_png(f"plot-{THEME}.png")
with open(f"plot-{THEME}.html", "wb") as f:
f.write(chart.render())
Part of Meta-Analysis Funnel Plot for Publication Bias on anyplot.ai.