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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 86/100 | Created: 2026-06-10
library(ggplot2)
library(ragg)
set.seed(42)
# --- Theme tokens ---
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
INK_MUTED <- if (THEME == "light") "#6B6A63" else "#A8A79F"
# Imprint palette — first categorical series always #009E73
IMPRINT_PALETTE <- c(
"#009E73", # 1 — brand green
"#C475FD", # 2 — lavender
"#4467A3", # 3 — blue
"#BD8233", # 4 — ochre
"#AE3030", # 5 — matte red
"#2ABCCD", # 6 — cyan
"#954477", # 7 — rose
"#99B314" # 8 — lime
)
# --- Data: 20 RCTs on antihypertensive treatment vs. placebo ---------------
n_studies <- 20
pooled_lor <- 0.45 # pooled log odds ratio (treatment reduces cardiovascular risk)
se_values <- c(
0.08, 0.10, 0.12, 0.14, 0.17, 0.19, 0.21, 0.24, 0.27, 0.30,
0.33, 0.36, 0.39, 0.42, 0.45, 0.48, 0.52, 0.55, 0.59, 0.63
)
# Slight funnel asymmetry: small studies tend toward larger effect (publication bias)
bias <- 0.22 * se_values
log_ors <- pooled_lor + bias + rnorm(n_studies, mean = 0, sd = se_values * 0.75)
studies <- data.frame(
log_or = log_ors,
std_error = se_values,
stringsAsFactors = FALSE
)
# Pseudo 95% CI funnel boundaries (pooled_lor ± 1.96 * SE)
max_se <- max(se_values) * 1.08
se_seq <- seq(0, max_se, length.out = 300)
funnel_lines <- data.frame(
se = rep(se_seq, 2),
x = c(pooled_lor - 1.96 * se_seq, pooled_lor + 1.96 * se_seq),
side = rep(c("lower", "upper"), each = length(se_seq))
)
# Closed polygon for shaded funnel region
funnel_poly <- data.frame(
x = c(pooled_lor - 1.96 * se_seq, rev(pooled_lor + 1.96 * se_seq)),
se = c(se_seq, rev(se_seq))
)
# --- Plot ---
title_str <- "funnel-meta-analysis · r · ggplot2 · anyplot.ai"
title_size <- round(12 * min(1.0, 67 / nchar(title_str)))
p <- ggplot() +
# Shaded funnel region
geom_polygon(
data = funnel_poly,
aes(x = x, y = se),
fill = IMPRINT_PALETTE[3],
alpha = 0.09,
color = NA
) +
# Funnel boundary lines (pseudo 95% CI)
geom_line(
data = funnel_lines,
aes(x = x, y = se, group = side),
color = IMPRINT_PALETTE[3],
linewidth = 0.7,
linetype = "dashed"
) +
# Null effect reference line (log OR = 0)
geom_vline(
xintercept = 0,
color = INK_MUTED,
linewidth = 0.5,
linetype = "dotted"
) +
# Pooled effect line
geom_vline(
xintercept = pooled_lor,
color = INK,
linewidth = 0.8
) +
# Study points (filled circles, edge matches page background for definition)
geom_point(
data = studies,
aes(x = log_or, y = std_error),
fill = IMPRINT_PALETTE[1],
color = PAGE_BG,
shape = 21,
size = 3.5,
stroke = 0.7,
alpha = 0.9
) +
# Invert y-axis: SE = 0 (most precise) at top, largest SE at bottom
scale_y_reverse(
expand = expansion(mult = c(0.02, 0.08))
) +
labs(
x = "Log Odds Ratio",
y = "Standard Error",
title = title_str,
subtitle = "Publication bias assessment — 20 RCTs on antihypertensive treatment vs. placebo",
caption = sprintf(
"n = %d studies · pooled log OR = %.2f · dashed funnel = pseudo 95%% CI",
n_studies, pooled_lor
)
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = INK_MUTED, linewidth = 0.25),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
axis.line = element_line(color = INK_SOFT, linewidth = 0.5),
plot.title = element_text(color = INK, size = title_size, face = "bold"),
plot.subtitle = element_text(color = INK_SOFT, size = 9),
plot.caption = element_text(color = INK_MUTED, size = 7, hjust = 1),
plot.margin = margin(t = 16, r = 20, b = 12, l = 14, unit = "pt")
)
# --- Save ---
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/funnel-meta-analysis/ggplot2/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": "r",
"library": "ggplot2",
"page": "https://anyplot.ai/funnel-meta-analysis/r/ggplot2",
"hub": "https://anyplot.ai/funnel-meta-analysis",
"code_json": "https://api.anyplot.ai/specs/funnel-meta-analysis/ggplot2/code",
"spec_json": "https://api.anyplot.ai/specs/funnel-meta-analysis",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/funnel-meta-analysis/r/ggplot2/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/funnel-meta-analysis/r/ggplot2/plot-dark.png",
"quality_score": 86.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Meta-Analysis Funnel Plot for Publication Bias on anyplot.ai.