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Meta-Analysis
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Professional systematic review tool validated against R metafor across core statistical methods — pooling, heterogeneity, bias detection, and network analysis. No R. No SPSS. Just your browser.

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18
Methods Validated
vs R
metafor Verified
35+
Features
0
Install Required
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
⚠ 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.

// Numerical comparison — Metovix v3 vs R metafor · dat.bcg · k=13 · log(RR) scale

Metric R metafor Metovix v3 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
🕸️
Advanced
  • Influence diagnostics (Cook's d)
  • Subgroup Q-between
  • Meta-regression (slope)
  • Cumulative meta-analysis
  • FE NMA — Rücker (2012)
  • RE NMA — Jackson (2012) τ²
  • Jacobi SVD pseudoinverse
  • Exact Hedges J via lgamma
📋 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: Metovix solves Q(τ²) = k−1 per Paule & Mandel (1982). R applies a proprietary correction. † Egger's test: Metovix 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).
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
📣
12 Bias Tests
Egger, Begg, Peters, Harbord, Macaskill, PET-PEESE, Trim-and-Fill, Fail-safe N, Selection Model.
Funnel PlotContour
🕸️
Network Meta-Analysis
Rücker (2012) graph-theoretic FE + Jackson (2012) RE. P-scores, league table, inconsistency check, network plot.
FE + REP-scoresSUCRA
🎨
12 Visualizations
Forest, Funnel, L'Abbé, Galbraith, Baujat, GOSH, Drapery, Cumulative, NNT, Network, Dose-Response, TSA.
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 DOCX/PDF/HTML reports with methods section, results, and PRISMA-compliant language ready for journal submission.
DOCXPDFHTML
📉
Dose-Response Analysis
Greenland-Longnecker two-stage method. Linear, quadratic, and restricted cubic spline models with CI bands.
LinearSplineRCS
💡
17-Format Export
CSV, JSON, Excel, DOCX, PDF, PNG, SVG, RTF, BibTeX, RIS, STATA do-file, R script, and more.
17 formatsBatch 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 ± tk-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) = χ²0.975,k-1
Q(τ²_hi) = χ²0.025,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 ± tk-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 = BᵀWB  // Laplacian
// Jacobi SVD pseudoinverse
L+ = V·D+·Vᵀ
μ = L+BᵀWy  // 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(tk-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%
Tool Comparison

More Features. Fraction of the Cost.

Metovix vs the most popular meta-analysis tools used by researchers worldwide.

Feature Metovix 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/PDF Limited ✗ Manual
Publication bias tests ✓ 12 tests ✓ 6 tests 2 tests ✓ 12+
Validated vs R metafor ✓ Verified
Core methods match		 Not public Separate ✓ IS R
Price Free / $29 / $49 $1,295/yr Free Free
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  • Up to 3 studies
  • OR, RR, MD effect measures
  • Forest plot + basic funnel
  • DL & FE pooling
  • Watermarked PDF export
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For PhD students and active researchers. Billed monthly.
  • Unlimited studies
  • All 10 effect measures
  • All 4 tau² estimators (DL, REML, PM)
  • All 12 publication bias tests
  • Cochrane ROB 2.0 & GRADE
  • Auto report generator (DOCX/PDF)
  • All 17 export formats
  • Priority support
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$49/mo
$98
50% OFF
For researchers needing advanced analysis. All features unlocked.
  • Everything in Researcher
  • Network Meta-Analysis (FE + RE)
  • Dose-Response Analysis
  • QUADAS-2 Diagnostic Accuracy
  • Three-level meta-analysis
  • Bayesian meta-analysis
💡 Annual billing saves ~2 months — $290/yr (Researcher) · $490/yr (Advanced)
Early Feedback

Researchers Love It

★★★★★
"I switched from R metafor to Metovix and the results are identical — in a fraction of the time. The forest plots are publication-ready out of the box."
SA
Dr. Sarah A.
Senior Researcher, Clinical Epidemiology
★★★★★
"As a medical student doing my first systematic review, I was overwhelmed by R. Metovix let me focus on the research, not the code. The GRADE profile feature alone is worth it."
MK
Mohammed K.
MBBS Student, Cochrane Author
★★★★★
"We switched our entire lab from CMA to Metovix. We saved $3,000/year and gained features like NMA and dose-response that CMA doesn't even have."
LP
Prof. Laura P.
Head of Systematic Reviews Lab
FAQ

Common Questions

Is Metovix 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 confidence intervals, prediction intervals, and HKSJ 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. Metovix 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 Metovix suitable for unpublished data and sensitive clinical information.
Can I use Metovix 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. Results match R metafor, which is widely cited and accepted by peer reviewers.
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, Dose-Response Analysis, QUADAS-2, three-level meta-analysis, Bayesian analysis, and Bayesian 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.
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