name: bio-data-visualization-forest-funnel-plots description: Build forest plots (HR, OR, RR, beta-coefficient summaries with CIs) and funnel plots (meta-analysis publication-bias diagnostics) using forestplot, metafor, ggforest, and MendelianRandomization with proper axis-scaling, summary-diamond placement, subgroup nesting, and Egger / trim-and-fill asymmetry tests. Use when summarizing effects across subgroups, trials, or instruments — meta-analysis, Mendelian randomization, subgroup HRs. origin: openai4s category: bioskills/data-visualization metadata: tool_type: r primary_tool: metafor third_party: name: GPTomics/bioSkills repository: https://github.com/GPTomics/bioSkills commit: d91ed3d563019e649dc854c56ccd62551359488a license: MIT
Reference examples tested with: metafor 4.4+, forestplot 3.1+, ggforestplot 0.1+ (subgroup forests), ggforest from survminer 0.4.9+, MendelianRandomization 0.10+.
Before using code patterns, verify installed versions match. If versions differ:
- R: packageVersion('<pkg>') then ?function_name
If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.
"Summarize effects across studies / subgroups" -> Render each effect estimate (HR, OR, RR, β) as a square (size = inverse variance / weight), horizontal bar (95% CI), and label, with an optional summary diamond at the bottom from a meta-analysis pool (fixed-effect or random-effects). The funnel plot diagnoses publication bias by plotting effect size vs precision; asymmetry indicates missing small-study-with-null-result publications (Egger 1997).
metafor::forest, metafor::funnel, forestplot::forestplot, survminer::ggforest (Cox HR forests), MendelianRandomization::mr_forestA pooled effect estimate is meaningless if the underlying studies are heterogeneous. The Higgins I² statistic (Higgins-Thompson 2002 Stat Med 21:1539) quantifies between-study variance; the conventional 25/50/75% interpretation tiers come from the Cochrane Handbook §10.10.2 (Higgins et al editors), NOT the original Higgins-Thompson paper which cautioned against rigid cutoffs. A meta-analysis with I² > 75% and a pooled effect must explain the heterogeneity (subgroup analysis, meta-regression) — pooling without explanation is statistically defensible but biologically unhelpful.
A forest plot's bottom must report: pooled estimate + 95% CI + I² + τ² (between-study variance) + Q-test p-value. Without these, the plot is a list of effects, not a meta-analysis.
| Analysis | Tool | Pooling model | Forest method |
|---|---|---|---|
| Single-trial subgroup HRs | survminer::ggforest | None (subgroup display) | Coxph object |
| Meta-analysis of binary outcomes | metafor::rma -> forest() | DerSimonian-Laird or REML random-effects | Standard forest |
| Meta-analysis of continuous outcomes | metafor::rma(yi, vi) | REML random-effects | Standard forest |
| Mendelian randomization | MendelianRandomization::mr_forest | Multiple MR methods | MR-specific forest |
| Subgroup forest with interaction p | metafor::rma + addpoly + interaction model | Subgroup REML | Nested forest |
| Network meta-analysis | netmeta::forest.netmeta | Bayesian or frequentist | Network forest |
| Cumulative meta-analysis (over time) | metafor::cumul + forest | – | Cumulative forest |
| Model | Assumption | When appropriate | Pooled estimate weight |
|---|---|---|---|
| Fixed-effect (Mantel-Haenszel, IVS) | All studies estimate the same true effect | Single mechanism, homogeneous design | 1 / within-study variance |
| Random-effects (DerSimonian-Laird, REML) | Studies estimate distinct true effects from a common distribution | Heterogeneous designs / populations | 1 / (within + between variance) |
Use random-effects by default. Fixed-effect assumes all studies estimate the same parameter, which is almost never true across multi-center trials with different populations. REML is the modern default (Viechtbauer 2005); DerSimonian-Laird is the older default still commonly seen.
Goal: Pool study-level effect estimates with random-effects meta-analysis; render a forest plot with study weights, individual effect+CI, and pooled summary diamond.
Approach: Compute per-study yi (effect) and vi (sampling variance); fit REML random-effects model; pass to forest() with prediction interval if heterogeneity is non-trivial.
library(metafor)
# Input: per-study effect (yi) and variance (vi)
# For OR: yi = log(OR), vi = SE(log(OR))^2
# For HR: yi = log(HR), vi = SE(log(HR))^2
res <- rma(yi = log_or, vi = log_or_se^2,
data = studies, slab = paste(author, year),
method = 'REML')
# I^2 and tau^2 in the summary
summary(res)
# I^2 (residual heterogeneity)
# tau^2 (estimated amount of (residual) heterogeneity)
# Q-test for heterogeneity
forest(res,
atransf = exp, # display OR on natural scale
at = log(c(0.25, 0.5, 1, 2, 4)), # ticks at meaningful OR values
refline = 0, # log(1) for OR/HR/RR
xlab = 'Odds Ratio (95% CI)',
header = c('Study', 'OR [95% CI]'),
mlab = bquote(paste('RE Model (Q = ', .(round(res$QE, 2)),
', df = ', .(res$k - 1),
', p = ', .(format.pval(res$QEp, digits = 2)),
'; ', I^2, ' = ', .(round(res$I2, 1)), '%)')),
addpred = TRUE) # prediction interval per Higgins 2009
addpred = TRUE adds a 95% prediction interval — where a new study's effect is expected to fall (Higgins-Thompson-Spiegelhalter 2009 JRSS-A). This is the most honest summary when I² > 30%.
library(survminer)
fit <- coxph(Surv(time, status) ~ treatment + age + sex + stage, data = df)
ggforest(fit,
data = df,
main = 'Subgroup HRs',
cpositions = c(0.02, 0.22, 0.4),
fontsize = 0.7,
refLabel = 'Reference',
noDigits = 2)
ggforest produces a publication-ready subgroup forest from a coxph object. For pre-specified subgroup analyses (treatment × subgroup interaction), test interaction explicitly and annotate the p-value.
For k < 5 studies, the REML-based 95% CI from metafor::rma() is severely anti-conservative — it relies on chi-square asymptotics that fail with few studies. Use Hartung-Knapp-Sidik-Jonkman (HKSJ) adjustment (test = 'knha'):
res_hksj <- rma(yi = log_or, vi = log_or_se^2, data = studies,
method = 'REML', test = 'knha') # HKSJ for k<5
HKSJ uses a t-distribution with k-1 degrees of freedom and adjusts SE via the Q-statistic — well-calibrated even at k=3. For k < 3 a meta-analysis is not advisable; report individual study effects in a forest plot without a pooled summary.
Also: I² is uninterpretable below k = 5 (Borenstein 2017 Res Synth Methods 8:5); the point estimate has wide CI dominated by k itself, not heterogeneity. Do not report I² for k < 5.
Goal: Diagnose publication bias by visual asymmetry of effect size vs precision.
Approach: Plot effect (x) vs SE (inverted y); under no bias, points form a symmetric inverted funnel with the pooled estimate at the apex. Asymmetry suggests missing small-N null-result studies. Egger's regression test (Egger 1997 BMJ 315:629) formalizes the asymmetry.
funnel(res,
xlab = 'log(OR)',
refline = res$b)
# Egger's test
regtest(res, model = 'lm', predictor = 'sei')
# significant p indicates asymmetry; suggests publication bias
# Trim-and-fill (Duval-Tweedie 2000) -- adjusts for asymmetry
res_tf <- trimfill(res)
forest(res_tf)
funnel(res_tf)
Contour-enhanced funnel plot (Peters 2008 J Clin Epidemiol 61:991) overlays significance contours (p < 0.10, < 0.05, < 0.01); asymmetry concentrated in "non-significant" regions indicates publication bias more specifically than generic asymmetry.
funnel(res, level = c(90, 95, 99), shade = c('white', 'gray55', 'gray75'),
refline = 0, legend = TRUE)
Trigger: Random-effects meta-analysis pooled with I² > 75%; no subgroup or meta-regression.
Mechanism: Pooled estimate is a weighted average across substantively different effects; biologically meaningless.
Symptom: Pooled OR = 1.5 with 95% CI (1.2-1.8) but per-study effects range 0.3-5.0.
Fix: Run subgroup analysis or meta-regression to explain heterogeneity; report I², τ², and prediction interval; do NOT report a single pooled effect as the answer.
Trigger: Default fixed-effect model on multi-population data.
Mechanism: Fixed-effect weights = 1/within-study variance, ignoring between-study variance.
Symptom: CI is misleadingly narrow; reviewer asks "why fixed effect with high I²?"
Fix: Switch to REML random-effects (method = 'REML'); document the choice.
Trigger: k < 10 studies; significant Egger p taken as definitive publication bias.
Mechanism: Egger's test is underpowered with few studies; sensitive to single outliers.
Symptom: Conclusion "publication bias" from k=6 trials.
Fix: Egger requires k ≥ 10 (Sterne 2011 BMJ 343:d4002); for fewer studies, visual funnel + contour-enhanced funnel is more reliable.
Trigger: Reporting trim-and-fill adjusted estimate as "the answer."
Mechanism: Trim-and-fill is a sensitivity analysis; imputed studies are hypothetical.
Symptom: Original pooled OR = 2.0; trim-and-fill adjusted to 1.5; report says "adjusted estimate is 1.5."
Fix: Present original AND trim-and-fill side-by-side; trim-and-fill is sensitivity, not primary.
Trigger: Subgroup HRs plotted; conclusion "treatment works in subgroup X."
Mechanism: Visual differences across subgroups don't establish significant interaction.
Symptom: Subgroup forest shows HR=0.5 in subgroup A, HR=1.0 in subgroup B; no formal test.
Fix: Add treatment × subgroup interaction term to the model; report interaction p; cite Brookes 2001 / Wang 2007 for subgroup analysis caveats.
Trigger: OR/HR/RR plotted with linear x-axis.
Mechanism: Ratios are multiplicatively symmetric; linear axis compresses < 1 effects.
Symptom: OR = 0.5 (halving) appears smaller than OR = 2 (doubling) on a linear scale, even though they are biologically equivalent.
Fix: Always log-scale the x-axis for ratios. metafor's atransf = exp + at = log(c(0.25, 0.5, 1, 2, 4)) is the canonical pattern.
Trigger: Default forestplot package without weight encoding.
Mechanism: Reader cannot tell study influence on pool.
Symptom: A 5-patient pilot looks visually equivalent to a 5000-patient trial.
Fix: Use metafor forest() which auto-encodes weight via box size. forestplot package needs boxsize = argument.
| Pattern | Cause | Action |
|---|---|---|
| Fixed-effect significant; random-effects n.s. | High heterogeneity inflates RE variance | Trust random-effects when I² > 30% |
| Egger n.s. but funnel looks asymmetric | k < 10 -> Egger underpowered | Trust visual; report contour-enhanced funnel |
| Trim-and-fill imputes many studies | Severe asymmetry | Caution; sensitivity, not primary |
| Subgroup forest suggests effect modification; interaction test n.s. | Visual difference does not establish formal interaction | Trust interaction test |
| MR forest shows divergent estimates across methods | Pleiotropy or weak instruments | Run MR-Egger, weighted median, mode-based (sensitivity); cite Bowden 2015 |
| Threshold | Value | Source |
|---|---|---|
| I² substantial heterogeneity | > 50% | Cochrane Handbook §10.10.2 (Higgins et al editors) |
| I² considerable heterogeneity | > 75% | Cochrane Handbook §10.10.2 (Higgins et al editors) |
| Egger test min k | ≥ 10 | Sterne 2011 BMJ |
| Prediction interval (where new study lands) | report when I² > 30% | Higgins-Thompson-Spiegelhalter 2009 |
| Forest x-axis | log scale for ratios | Convention |
| Error / symptom | Cause | Solution |
|---|---|---|
| Pooled estimate with I² = 90% | No heterogeneity exploration | Subgroup / meta-regression |
| Linear x-axis for OR forest | Ratios should be log-symmetric | atransf = exp, at = log(...) |
| Uniform point sizes | Weights not encoded | metafor::forest auto-encodes; forestplot needs boxsize |
| Egger from k=5 | Underpowered | k ≥ 10 for Egger |
| Trim-and-fill as primary | Sensitivity, not primary | Present both; document |
| Subgroup effect without interaction test | Visual ≠ test | Add interaction term |
| MR forest with single method | Pleiotropy risk | Triangulate methods |