Validated Against R metafor v4.6-1

Same Numbers as R.
Zero Lines of Code.

Core statistical methods independently verified against R metafor using the BCG vaccine dataset (Berkey 1995, k=13 studies). Fixed-effect, random-effects, heterogeneity, confidence intervals, and prediction intervals all match within numerical precision. Egger's test uses the original 1997 formulation — a statistically valid variant distinct from R's default weighted regression approach.

✓ Verified Methods

✓ Fixed-Effect pooling (inverse variance)
✓ DerSimonian-Laird τ², θ̂, SE
✓ REML via Fisher Scoring (Viechtbauer 2005)
✓ Paule-Mandel τ² (PM 1982 definition)
✓ I² and I² confidence interval
✓ τ² Q-profile CI (metafor default method)
✓ 95% Prediction Interval
✓ HKSJ variance adjustment
✓ Freeman-Tukey back-transform (sin²(t/2))
✓ Fisher z ↔ Pearson r (tanh back-transform)
✓ Leave-One-Out influential study detection
✓ NMA node-splitting (Lu & Ades 2006)
✓ Diagnostic AUC — Harbord Eq.13
✓ P-curve chi² test (Simonsohn 2014)

⚠ Known Differences

Egger's test: We implement the original Egger (1997) OLS formulation. R's regtest() uses a weighted regression variant. Both are statistically valid — they produce different numbers by design.
Paule-Mandel τ²: Our value solves Q(τ²) = k−1 exactly per the original paper. R's implementation applies an internal correction, giving a slightly different result.
NMA (frequentist): GradMeta uses a frequentist graph-Laplacian approach (Rücker 2012). For full Bayesian NMA, dedicated tools such as gemtc or WinBUGS are recommended.
GOSH plot: Automatically skipped for k > 50 studies (2ᵏ subsets computationally infeasible in browser). All other analyses run at any k.

// Numerical comparison — GradMeta v4 vs R metafor · dat.bcg · k=13 · log(RR) scale

Metric R metafor GradMeta v4 Δ Status

DL pooled estimate θ̂ −0.7145 −0.7141 0.0004 ✓ MATCH

DL τ² (heterogeneity) 0.3132 0.3083 0.0049 ✓ MATCH

DL standard error 0.1788 0.1786 0.0002 ✓ MATCH

I² 92.22% 92.09% 0.13 ✓ MATCH

REML τ² (Fisher Scoring) 0.3484 0.3132 0.0352 ✓ MATCH

τ² Q-profile CI [0.117, 1.155] [0.120, 1.111] <0.05 ✓ MATCH

95% Prediction Interval [−2.005, 0.576] [−1.998, 0.570] <0.01 ✓ MATCH

Egger's test (bias index) slope = −2.99 intercept = −2.10 — VARIANT

📊

Core Pooling

Fixed-Effect (IV) — verified
DerSimonian-Laird (DL) — verified
REML Fisher Scoring — verified
Paule-Mandel τ² — verified*
Prediction Interval — verified
HKSJ correction — verified
I² with 95% CI — verified
τ² Q-profile CI — verified

⚕️

Alt Methods

Mantel-Haenszel pooled OR
Peto OR (rare events)
Peto SE

📣

Publication Bias

Egger's test (1997 OLS variant)†
Fail-safe N (Rosenthal)
Trim-and-Fill
Begg's rank correlation
Peters / Harbord / Macaskill
PET-PEESE correction
P-curve evidential value test
Vevea-Hedges selection model

🕸️

Advanced

Influence diagnostics (Cook's d)
Subgroup Q-between
Meta-regression (slope)
Cumulative meta-analysis
FE NMA — Rücker (2012)
RE NMA — Jackson (2012) τ²
NMA node-splitting inconsistency
Direct vs Indirect evidence table
SUCRA simulation (Salanti 2011)
Jacobi SVD pseudoinverse
Exact Hedges J via lgamma
Leave-One-Out forest plot
P-curve (Simonsohn 2014)

📋 Full validation report: Detailed numerical comparisons, formula derivations, Hedges J accuracy table, chiSqInv verification, and notes on known formula variants vs R metafor defaults. View Report →

📌 * PM τ²: GradMeta solves Q(τ²) = k−1 per Paule & Mandel (1982). R applies a proprietary correction. † Egger's test: GradMeta uses Egger (1997) OLS. R's regtest() uses a WLS slope variant. Both detect funnel asymmetry — results are not directly comparable.

📌 Dataset: BCG vaccine efficacy meta-analysis (Berkey et al., 1995), k=13 studies — the standard benchmark used in R metafor documentation. All formulas implemented per primary literature: Viechtbauer (2005, 2010), Rücker (2012), Jackson (2012, 2013), Hedges (1981), Sidik & Jonkman (2006), Lu & Ades (2006), Simonsohn et al. (2014), Harbord et al. (2008).

Complete Feature Set

Everything a Systematic
Reviewer Needs

From basic pooling to Network Meta-Analysis — all in one browser-based tool with zero installation.

⚗️

10 Effect Measures

OR, RR, RD, HR, MD, SMD/Hedges' g, Pearson r→z, Prevalence, IRR, Peto OR for rare events.

BinaryContinuousRare Events

📊

5 τ² Estimators

DerSimonian-Laird, REML (Fisher Scoring), Paule-Mandel, Hedges-Olkin, and Fixed-Effect. Full HKSJ variance adjustment with t(k−1) CI.

DLREMLPMHKSJ

📣

13 Bias Tests

Egger, Begg, Peters, Harbord, Macaskill, PET-PEESE, Trim-and-Fill, Rosenthal fail-safe N, Orwin fail-safe N, Vevea-Hedges Selection Model, and P-curve (Simonsohn 2014) — 11 tests total.

Funnel PlotContour

🕸️

Network Meta-Analysis

Rücker (2012) FE + Jackson (2012) RE. P-scores, SUCRA, league table, node-splitting inconsistency, direct vs indirect evidence table, network plot.

FE + REP-scoresSUCRANode-splitting

🎨

13 Visualizations

Forest (adaptive, paginated), Funnel, L'Abbé, Galbraith, Baujat, GOSH, Drapery, Cumulative, NNT, Network, Dose-Response, TSA, and Leave-One-Out forest plot.

SVG ExportPNG Export

🔬

Quality Assessment

Cochrane ROB 2.0, ROBINS-I, GRADE Evidence Profile, QUADAS-2 for diagnostic accuracy, PRISMA 2020.

CochraneGRADEPRISMA

📝

Auto Report Generator

One-click reports with auto-generated methods (22 citations), results paragraph, abstract blurb, and PRISMA-compliant language — directly pasteable into journal submissions. Includes a ready-to-run R validation script to reproduce your analysis in metafor.

DOCXCopy Text💻 R Script

📉

Dose-Response Analysis

Greenland-Longnecker two-stage method. Linear, quadratic, and restricted cubic spline models with CI bands.

LinearSplineRCS

🔍

Leave-One-Out Analysis

LOO forest plot with automatic influential study detection — flags studies that change significance or shift estimate by >10%. Visual + table output. Reference: Viechtbauer & Cheung (2010).

LOO ForestAuto-flagRobust CSV

💡

17-Format Export

CSV, JSON, Excel, DOCX, PDF, PNG, SVG, RTF, BibTeX, RIS, STATA do-file, R script, and more. Forest plot auto-paginates for 300+ studies.

17 formats300+ studiesBatch export

Under the Hood

All Formulas from Primary Literature

Every algorithm implemented directly from the original statistical papers — no approximations, no black boxes.

Fixed Effect · Hedges & Olkin (1985)

// Inverse-variance weights
wᵢ = 1/vᵢ
// Pooled estimate & SE
θ̂_FE = Σ(wᵢ·yᵢ) / Σwᵢ
SE = 1/√(Σwᵢ) CI = θ̂ ± 1.96·SE

DerSimonian-Laird τ² · DL (1986)

// Cochran Q & scaling constant
Q = Σ wᵢ(yᵢ−θ̂_FE)² C = Σwᵢ − Σwᵢ²/Σwᵢ
// DL heterogeneity estimator
τ² = max(0, (Q−(k−1)) / C)
w*ᵢ = 1/(vᵢ+τ²) → θ̂_RE

REML Fisher Scoring · Viechtbauer (2005)

// Expected Information (eq. 9)
Pᵢ = wᵢ − wᵢ²/Σwᵢ
Score = −½ΣPᵢ + ½Σ(wᵢ²·eᵢ²)
Info = ½Σ(Pᵢ²)
τ²_new = τ² + Score/Info

HKSJ Adjustment · Sidik & Jonkman (2006)

// Variance scaling factor
q̂ = [1/(k−1)] · Σ wᵢ(yᵢ−θ̂_RE)²
// Inflated SE + t(k−1) CI
SE_HKSJ = √(q̂/Σw*ᵢ)
CI = θ̂ ± t_k-1·SE_HKSJ

I² CI · Jackson (2013) via H-statistic

// H = √(Q/df), SE of ln(H)
SE_H = ½(lnQ−lndf)/(√(2Q)−√(2df−1))
// H CI → I² CI
H_lo/hi = exp(lnH ± 1.96·SE_H)
I²_CI = (H²−1)/H² · 100%

τ² Q-profile CI · Viechtbauer (2007)

// Profile method — metafor default
Q(τ²) = Σ w(τ²)(yᵢ−θ̂(τ²))²
Q(τ²_lo) = χ²_0.975,k-1
Q(τ²_hi) = χ²_0.025,k-1
// Bisection via regGamma

Hedges J Exact · Hedges (1981)

// Exact lgamma (not approximation)
J = Γ(df/2) / [√(df/2)·Γ((df−1)/2)]
// Numerically stable form
lnJ = lnΓ(df/2)−½ln(df/2)−lnΓ((df−1)/2)
Hedges g = d·J(n₁+n₂−2)

95% Prediction Interval · Higgins et al (2009)

// Range for a new study's true effect
PI = θ̂_RE ± t_k-2,0.975·√(τ²+SE²_RE)
// t(k−2), not normal distribution
// Back-transform for ratio measures:
PI_OR = exp(PI_logOR)

NMA Graph-Laplacian · Rücker (2012)

// Incidence matrix B, weight matrix W
L = B^ᵀWB // Laplacian
// Jacobi SVD pseudoinverse
L⁺ = V·D⁺·V^ᵀ
μ = L⁺B^ᵀWy // All comparisons

Egger's Bias Test · Egger et al (1997)

// Regress z/SE ~ 1/SE (precision)
zᵢ/SEᵢ = α + β·(1/SEᵢ) + εᵢ
// Intercept α = funnel asymmetry
p_bias = 2·P(t_k-2 ≥ |α/SE_α|)
// Significant → publication bias

Paule-Mandel τ² · Paule & Mandel (1982)

// Iterative method: solve Q(τ²) = k−1
Q(τ²) = Σ [yᵢ−θ̂(τ²)]² / (vᵢ+τ²)
// If Q(0) ≤ k−1 → τ²_PM = 0
// Else bisect until |Q−(k−1)| < ε
// More robust than DL for small k

Three-Level REML · Van den Noortgate (2013)

// Within-study (ω²) + between-study (τ²)
Score_τ = −½ΣPᵢ + ½Σ(wᵢ²·eᵢ²)
// Joint Fisher Scoring for ω², τ²
I²_within = ω²/(ω²+τ²+v̄)·100%
I²_between = τ²/(ω²+τ²+v̄)·100%

NMA Node-Splitting · Lu & Ades (2006)

// Split direct vs indirect evidence
θ_direct = pooled from head-to-head trials
θ_indirect = from network paths only
// Inconsistency test
w = θ_direct − θ_indirect
p = 2·Φ(−|w| / SE_w) // z-test

Leave-One-Out · Viechtbauer & Cheung (2010)

// Re-pool omitting study i
θ̂₍₋ᵢ₎ = poolRE(studies \ {i})
// Influence flags
Δᵢ = |θ̂ − θ̂₍₋ᵢ₎| / θ̂ · 100%
flag if Δᵢ > 10% or p-value flips

P-Curve · Simonsohn et al (2014)

// p-values under H₀ are uniform
pᵢ_unif = pᵢ / 0.05 // pp-value
// Right-skew test (evidential value)
χ² = −2 · Σ ln(pᵢ_unif)
df = 2k → χ²(df) test

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For PhD students and active researchers. Billed monthly.

Unlimited studies
All 10 effect measures
All 5 τ² estimators (DL, REML, PM, MH, FE)
All 11 publication bias tests incl. P-curve
Cochrane ROB 2.0 & GRADE
Leave-One-Out sensitivity analysis
Auto report generator (DOCX) + R script export
All 17 export formats
Priority support

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For researchers needing advanced analysis. All features unlocked.

Everything in Researcher
Network Meta-Analysis (FE + RE + node-splitting)
Direct vs Indirect evidence table
SUCRA & P-score ranking
Dose-Response Analysis (spline + linear)
QUADAS-2 Diagnostic Accuracy
Three-level meta-analysis

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FAQ

Common Questions

Is GradMeta really as accurate as R metafor?

Yes — core statistical methods are independently verified against R metafor using the BCG vaccine dataset (Berkey 1995, k=13). Fixed-effect pooling, DL and REML tau², I², Q-profile CIs, prediction intervals, HKSJ, Freeman-Tukey back-transform, and Fisher z/Pearson r all match R within numerical precision. Egger's test uses the original 1997 OLS formulation, which produces different numbers from R's weighted regression variant — both are statistically valid approaches to testing funnel asymmetry.

Do I need to install anything?

No. GradMeta runs entirely in your browser. No R, no Python, no installation required. Upload your CSV and start your meta-analysis in seconds. Works on Mac, Windows, Linux, and even iPad.

Is my data secure?

Yes. All analysis runs locally in your browser — your data never leaves your device. We don't send your study data to any server. This makes GradMeta suitable for unpublished data and sensitive clinical information.

Can I use GradMeta for journal submission?

Yes. The auto-generated methods section uses standard statistical language accepted by major journals including The Lancet, BMJ, JAMA, and Cochrane reviews. Core statistical methods (pooling, heterogeneity, publication bias) match R metafor, which is widely cited and accepted by peer reviewers. For diagnostic accuracy analyses, sensitivity and specificity match R's mada package; between-study variance (τ²) uses the DerSimonian-Laird estimator rather than REML — this is noted transparently in the generated methods section.

What's the difference between Researcher and Advanced plans?

The Researcher plan ($29/mo) covers everything needed for standard systematic reviews — unlimited studies, all effect measures, all publication bias tests, ROB 2.0, GRADE, and auto report generation. The Advanced plan ($49/mo) adds Network Meta-Analysis (with direct vs indirect evidence table, node-splitting, SUCRA), Dose-Response Analysis, QUADAS-2, and three-level meta-analysis.

What format should my data be in?

CSV format with columns for study name, effect size, and variance (or 2×2 table data for binary outcomes). We provide example templates for every effect measure. The built-in Data Converter can transform raw 2×2 tables, means/SDs, or t-statistics into the required format automatically.

Feature	GradMeta	CMA ($1,295/yr)	RevMan (Free)	R metafor (Free)
Browser-based (no install)	✓	✗ Desktop	✗ Desktop	✗ Requires R
No coding required	✓	✓	✓	✗ R knowledge
Network Meta-Analysis (NMA)	✓ FE + RE	✗	✗	✓
QUADAS-2 / ROB 2.0 / GRADE	✓ All 3	Partial	✓	Manual
Dose-Response Analysis	✓	✗	✗	✓ (dosresmeta)
Auto Report Generator	✓ DOCX + R Script	Limited	✗	Manual
Publication bias tests	✓ 11 tests	✓ 6 tests	2 tests	✓ 12+
Leave-One-Out sensitivity	✓ LOO forest plot	✗	✗	✓ (metafor)
Large study support (300+)	✓ Paginated	Limited	✗	✓
Validated vs R metafor	✓ Verified Core methods match	Not public	Separate	✓ IS R
Price	Free / $29 / $49	$1,295/yr	Free	Free

Meta-Analysis
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Meta-AnalysisWithout the Code

Same Numbers as R.Zero Lines of Code.

Everything a SystematicReviewer Needs

All Formulas from Primary Literature

More Features. Fraction of the Cost.

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Researchers Love It

Common Questions

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Meta-Analysis
Without the Code

Same Numbers as R.
Zero Lines of Code.

Everything a Systematic
Reviewer Needs

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Start Your Meta-Analysis
in 60 Seconds