NMAViz

Read the evidence structure of a network meta-analysis, through the lenses the methods literature has proposed for it.

Upload the data behind an NMA and the site fits the frequentist graph-theoretical model in your browser, then draws that fitted model through eight linked lenses: as a map whose distances are standard errors, as trials rather than comparisons, as a flow of evidence, as a contribution matrix, as a signed reconstruction of the estimate trial by trial, as a decomposition of its inconsistency, as a diffusion, and as a system of springs.

A ninth, separate population laboratory fits editable individual and aggregate data for population adjustment. All analysis runs locally in the browser; selected files are not sent to a backend.

Open it at nmaviz.xera.ac

Where one estimate comes from	What each trial did to it
Inconsistency triangles can see, and cannot	Studies in parallel, routes in series

Most network meta-analysis software answers what the estimates are. This answers where they came from. The first eight lenses share the fitted contrast network and selected comparison. The Population lens has its own synthetic or imported individual and aggregate data; selecting it does not population-adjust the contrast network.

Each lens offers two numeric prediction challenges with corrective explanations and a session score (18 challenges total). These use stated teaching examples independently of imported research data. The spring wager hides the resting answer before submission; the population mission asks for the direction of a transported effect before revealing fitted outcomes. Hodge examples let learners compare a chordless cycle with a triangulated network.

Keyboard controls support trial exclusion and spring interaction. Dialogs trap focus, close with Escape, and restore focus to their opener. Practice feedback uses live status text; the mobile layout can expand the diagram within a scrollable region. These are implemented learning and accessibility features, not evidence that the app is universally accessible or educationally optimal.

A CSV or tab separated file, in either of the two shapes people have.

Contrast level, one row per comparison:

study,treat1,treat2,TE,seTE
Trial A,drug,placebo,-0.42,0.19

Arm level, one row per arm, either binary or continuous:

study,treatment,event,n            study,treatment,mean,sd,n

Arm-level data is converted with the same formulas netmeta::pairwise uses, including the continuity correction for a study with a zero cell. Common column names are recognized automatically (t1, lnOR, selnOR, trial, author, and so on), and the data panel shows the mapping it settled on.

A contrast-level file carries numbers but not the scale they are on, so the effect measure is guessed from the name of the effect column and defaults to the identity scale, where the numbers are shown exactly as the file gave them. The data panel names the guess and lets you correct it; correcting it matters, because a ratio measure is fitted on the log scale and shown exponentiated.

Pooled results alone cannot reconstruct the contrast-network evidence: its hat matrix requires study-level data. Population adjustment additionally requires the covariate and outcome inputs described below.

Thirteen example networks ship with the site, the full set distributed with the R package netmeta: three treatments to twenty-two, three studies to ninety-three, two-arm only to heavily multi-arm, and mean differences through odds and incidence rate ratios.

The JavaScript engine is checked against committed fixtures from netmeta 3.6.1 for six networks, including multi-arm studies. scripts/fixtures.R regenerates those model fixtures. Tests cover Laplacians, pseudoinverses, hat matrices, common/random estimates and SEs, direct/indirect estimates, heterogeneity, design Q decomposition, sorting, and multi-arm adjustments. Tolerances are specified in the tests; passing fixtures do not establish correctness for every possible input.

The supplied Linde2016 path-method matrices provide a separate reference for all L2 and random-walk entries. Shortest-path ties and nonunique L1 optima can give different valid allocations. L1 tests therefore certify flow reconstruction, nonnegativity and the minimum objective rather than require one solver's particular answer.

Structural and regression checks cover contrast reversal, covariance-aware random-effects reconstruction, canonical routes, flow conservation, bipartite block identities, Hodge orthogonality, spring equilibrium/energy, diffusion convergence, and input validation. Population tests include synthetic fits; numerical integration is checked against analytic moments, and posterior sampling against known normal and beta targets. These are not independent reproductions of every thesis case study or clinical validation.

npm test
npm run build
npx playwright install chromium
npm run test:browser

The browser script starts its own local Vite server. It exercises nine lenses, practice feedback, keyboard dialog focus and trial exclusion, four contribution methods, Hodge examples, diffusion, the spring wager, population fitting, and mobile expansion. Screenshots are written under documentation/implementation/browser/. Browser coverage is a set of concrete scenarios, not a complete accessibility or usability evaluation.

Node.js 22.13 or newer.

npm ci
npm run dev      # http://127.0.0.1:3021
npm run build
npm run preview

Regenerating the fixtures and the bundled examples needs R with netmeta and jsonlite:

Rscript scripts/fixtures.R
Rscript scripts/examples.R

Multi-arm studies. The model uses netmeta's reduce-weights adjustment, with τ² added before the adjustment. For coherent complete multi-arm contrasts and their covariance, this is equivalent to reduced-dimension GLS. Reconstruction uses the fitted weights and the full within-study covariance, including heterogeneity. Direct and indirect contributions remain correlated. Design-based Q components use compatible adjusted weights. Input validation rejects invalid or materially incoherent multi-arm data; rounded contrasts may leave a reported canonical-route effect residual.

Bipartite information flow. Signed treatment-trial coefficients reconstruct the contrast fit. Positive arm-precision transitions and the fixed-trial block identity require an independent-arm variance representation. Unsupported cases are identified instead of assigning invented transition probabilities. A two-arm contrast does not identify separate arm variances; its default equal split is an explicit convention, not recovered arm information.

Path optimization. L1/L2 enumerate at most 5,000 directed paths across at most 150 active comparisons. L1 uses a maximum of 10,000 iterations and requires a certified feasible optimum. Bounds or nonconvergence produce an error; choose shortest path or random walk for those networks. L2 can yield negative shares, which are retained. Canonical projection routes use a separate study-based direct-first and widest-first decomposition, not these contribution percentages.

The arrangement. The Laplacian pseudoinverse is a Gram matrix, so its principal coordinates place treatments where the straight-line distance between two of them is the standard error of the network estimate comparing them. Two dimensions cannot generally hold that, so stress majorization fits it as closely as a plane allows, overlapping circles are nudged apart, and the residual stress is measured on the drawing that is actually on screen and printed under the title.

Inconsistency. The Hodge split is computed on one pooled estimate per comparison. Disagreement between studies of the same comparison is heterogeneity, not inconsistency, and is not part of it. It is a diagnostic to read alongside a design-by-treatment interaction model, not a replacement for one. Its residual is the between-comparison Q, which need not equal netmeta's between-design Q; the interface names which quantity it is showing.

Harmonic dimension is structural. The harmonic space depends on network topology. When triangle boundaries span the cycle space, its dimension is zero and the lens says "none possible". That is not evidence that observed comparisons agree. The chordless four-cycle example demonstrates a network where harmonic inconsistency is possible.

What Papakonstantinou et al actually cover. Their paper is about pairwise meta-analysis, and says extending the spring system to a network is future work. Studies in parallel, the pooled estimate as the resting point, and the energy identity are theirs; routes in series, drawn from the flow decomposition, are this site's extension of the idea and are labeled as such.

Flow measures. The interface distinguishes comparison-edge path summaries from study/design measures. Design mean path length sums design flows; study and design minimal parallelism use the reciprocal of the corresponding maximum flow. They need not equal edge-based measures when multi-arm studies are present.

Ranking. Hodge potential and Borda scores are descriptive orderings. Exact Kemeny optimization is bounded to 12 treatments; the interface reports when it is unavailable. These are not SUCRA, rankograms, probabilities of being best, or a clinical recommendation.

The population editor accepts JSON containing IPD (study, treatment, x, y), aggregate records, a reference treatment and an optional target population. Covariates may be scalar or vectors. Aggregate binary records use n/events, normal records mean/se, ordinal records category counts, and survival records event/censoring times with covariates marginalized. Use the editable examples and JSON export for the full schema. Population data are separate from the CSV contrast import.

ML-NMR integrates individual response probabilities in the aggregate likelihood. Binary aggregate arms offer a one-parameter binomial approximation using E[p], or a two-parameter approximation matching the Poisson-binomial mean and variance with N* = n E[p]²/E[p²] and p* = E[p²]/E[p]. The latter uses a continuous-N binomial likelihood with gamma-function coefficients; it is an approximation, not the exact Poisson-binomial likelihood. Parameter proposals with N* below the observed event count have zero support.

STC fits IPD outcome regression and standardizes predictions. MAIC balances covariate means and reports effective sample size, weighted outcomes and bootstrap uncertainty with weights re-estimated in each resample; anchored comparison is conditional on matching the supplied aggregate target. MAIC requires overlap, and its bootstrap conditions on supplied target moments. MAIC supports binary and normal outcomes; it does not estimate ordinal or survival contrasts.

Population distributions may use empirical points, a uniform midpoint shortcut, or Sobol points with a Gaussian copula and normal, lognormal, uniform or Bernoulli marginals. Copula correlation is on the latent Gaussian scale. Integration diagnostics compare finite approximations, not guaranteed absolute error bounds. Unknown covariate distributions and measurement error are not inferred.

The fixed-effects fitter supports binary, normal, ordinal and Weibull survival likelihoods with one to five covariates and shared, independent or no effect modification. Normal sigma, ordinal cutpoints, Weibull shape and aggregate normal SEs are supplied as known. Limits are 2,000 IPD records, 100 aggregate records and 24 fitted coefficients. Approximate Wald SEs come from numerical observed information; nonidentifiability and optimizer diagnostics are displayed.

After a prediction, the inspector offers background Bayesian sampling with cancellation. Both fixed and hierarchical sampling default to four chains with 500 warmup and 1,000 retained draws per chain. The controls also offer 4,000 or 12,000 retained draws; JSON sampling.warmup and sampling.seed set warmup and reproducibility. Fixed-model sampling uses independent Normal(0, 2.5²) coefficient priors. Hierarchical controls select random/fixed effects, modifier structure and consistency/UME. Both sample the specified likelihood or aggregate approximation using Metropolis chains.

The hierarchical model supports a common heterogeneity SD with multi-arm covariance τ²/2 and shared, independent, exchangeable or no modifiers. Exchangeability uses one global class of active treatments. Normal coefficient and half-normal SD priors are proper and depend on covariate units. The backend is bounded to 40 parameters and two to eight chains. UME (unrelated mean effects) is available only for closed networks of two-arm trials; tree and multi-arm inputs are rejected.

Posterior target summaries include response, conditional-effect and binary marginal-log-OR intervals. Absolute predictions borrow an observed study baseline; they do not estimate a new target baseline or include a new-study random effect. Deviance omits data-only constants and is comparable only on the same data. Integration and posterior intervals condition on supplied population distributions and nuisance parameters.

Sampling reports classical split-R̂, ESS, MCSE and acceptance diagnostics. Short teaching runs can fail those checks; these are not rank-normalized diagnostics or a guarantee of convergence. The sampler is not a replacement for a validated production Bayesian workflow, and the examples do not reproduce the thesis's clinical trials or simulation studies.

The reference collection guides the implementations; this is not complete reproduction of every paper, thesis chapter, simulation and clinical case study. The app does not assess risk of bias, establish transitivity, identify all effect modifiers, or establish causal transportability. Zero inconsistency does not validate a network; large contribution does not mean high-quality evidence.

The app is static, with no account or login. Analysis files and population JSON are processed in the browser; the app does not send them to an analysis server. The theme choice is kept in local storage. Hosting infrastructure may separately log ordinary page requests.

MIT. Inter is licensed under the SIL Open Font License. The example networks are redistributed from the R package netmeta, which is GPL-2 licensed, with each network's original source cited in the data panel.

Method sources include:

• Rücker G. Network meta-analysis, electrical networks and graph theory. Res Synth Methods 2012;3(4):312-324.
• Senn S, Gavini F, Magrez D, Scheen A. Issues in performing a network meta-analysis. Stat Methods Med Res 2013;22(2):169-189.
• König J, Krahn U, Binder H. Visualizing the flow of evidence in network meta-analysis and characterizing mixed treatment comparisons. Stat Med 2013;32(30):5414-5429.
• Jiang X, Lim LH, Yao Y, Ye Y. Statistical ranking and combinatorial Hodge theory. Math Program 2011;127(1):203-244.
• Papakonstantinou T, Nikolakopoulou A, Egger M, Salanti G. Meta-analysis as a system of springs. Res Synth Methods 2021;12(2):176-186.
• Davies AL, Papakonstantinou T, Nikolakopoulou A, Rücker G, Galla T. Network meta-analysis and random walks. Stat Med 2022;41(12):2091-2114.
• Rücker G, Papakonstantinou T, Nikolakopoulou A, Schwarzer G, Galla T, Davies AL. Shortest path or random walks? A framework for path weights in network meta-analysis. Stat Med 2024;43(22):4287-4304.
• Davies AL. The bipartite structure of treatment-trial networks reveals the flow of information in network meta-analysis. J R Stat Soc Ser A 2026.
• Rücker G, Davies AL, Schwarzer G. Network meta-analysis and diffusion. Res Synth Methods 2026.
• Wang C, Zhang Y, Jin Z, O'Connor A. Contrast-space projection for network meta-analysis: an exact and invariant study-based decomposition of direct and indirect contributions. 2026.

The reference implementation this engine is tested against is Schwarzer G, Carpenter JR, Rücker G. netmeta: Network Meta-Analysis using Frequentist Methods, R package version 3.6.1.

The separate population laboratory draws on Phillippo DM, Population adjustment methods for indirect comparisons: a review and development of multilevel network meta-regression, PhD thesis. Its implemented scope and inference limits are described above.