LivingNMA

Living Network Meta-Analysis — Frequentist NMA, consistency, P-scores, league table, network evolution

Data Input

Network Graph

Results

League Table

Ranking

Consistency

Forest Plots

Net Heat

Contribution

Funnel

CINeMA

Direct vs NMA

All Pairs

Bayesian

Assessment

Guide

Load Example

Contrast-Level Data

One contrast per line: Study, Treatment1, Treatment2, Effect (T1 vs T2), SE. Effect on log scale for OR/RR/HR or raw for SMD. Treatment names are case-sensitive.

Effect measure

Reference treatment

Contrast data (study, trt1, trt2, effect_1vs2, SE)

Network Graph

Network Summary

All Pairwise Comparisons (vs Reference)

Comparison	Estimate	95% CI	95% PI	P-value	Direct?

Pairwise MA for Each Direct Comparison

For each edge in the network with 2+ studies, a standard pairwise random-effects meta-analysis (DerSimonian-Laird) is computed. Compares direct-only pooled estimate with the NMA estimate to quantify the indirect evidence contribution.

Heterogeneity Variance Decomposition

Compares common tau-squared (single value assumed across all comparisons) with comparison-specific tau-squared. Large variation across comparisons challenges the common heterogeneity assumption. Comparisons with tau-squared exceeding 2x the common value are flagged.

League Table

Row treatment vs column treatment. Green = statistically significant. Read: row is [estimate] compared to column. Amber text = 95% prediction interval (where a new study's effect might fall).

Treatment Rankings (P-scores & SUCRA)

Rank	Treatment	P-score	SUCRA	Mean Rank (95% CrI)	vs Reference	Rank Stability

Rankogram (Salanti et al. 2011) — Probability of Each Rank

Each row shows the probability of a treatment being at each rank position, computed from 1000 multivariate normal simulations of (beta, vcov). Darker color = higher probability. SUCRA = area under the cumulative ranking curve.

Consistency Assessment

Design-by-Treatment Interaction Test (Higgins et al. 2012)

Global inconsistency test: decomposes total Q into heterogeneity (within-design) and inconsistency (between-design) components. Unlike node-splitting (local), this is a single omnibus test. Q_inconsistency = Q_total - Q_heterogeneity, tested as chi-squared.

Component	Q	df	P-value	Interpretation

Node-Splitting (Local Inconsistency)

Comparison	Direct	Indirect	Difference	P-value	Verdict

SIDE Test (Separating Indirect from Direct Evidence, Koenig et al. 2013)

For each comparison with direct evidence, the SIDE test compares the direct estimate with the indirect estimate derived by subtracting the direct contribution from the NMA estimate. A significant z-test indicates disagreement between direct and indirect sources.

Comparison	Direct Est (SE)	Indirect Est (SE)	z-statistic	P-value	Verdict

Forest Plot — All Comparisons vs Reference

Net Heat Plot (Krahn et al. 2013)

Each cell (i,j) shows how much design i contributes to the NMA estimate for comparison j. Warm colors = high contribution. Red-bordered cells highlight inconsistency hotspots where removing that design changes the estimate substantially.

Contribution Matrix (Papakonstantinou et al. 2018)

For each NMA estimate (rows), shows what percentage comes from each direct comparison (columns). Higher percentages mean that direct comparison drives the NMA estimate more. Rows sum to 100%.

Information Fraction: Direct vs Indirect Evidence

For each NMA comparison with direct evidence, shows what percentage of information comes from direct vs indirect sources. Direct info = 1/Var(direct), Indirect info = 1/Var(indirect). Comparisons with less than 20% direct evidence are flagged.

Comparison-Adjusted Funnel Plot (Chaimani & Salanti 2012)

X-axis: study residual (observed effect minus NMA estimate for that comparison). Y-axis: standard error. Asymmetry around the zero line suggests small-study effects. Each color represents a different comparison.

Small-Study Effects Regression Test (Chaimani & Salanti 2012)

Comparison-adjusted Egger-like test: regresses study residuals (y_ij - d_ij) on SE with comparison indicators. A significant slope indicates asymmetry consistent with small-study effects or publication bias in the network.

CINeMA-Style Confidence Assessment (Nikolakopoulou et al. 2020)

Simplified automated assessment across 6 domains: Within-study bias, Reporting bias, Indirectness, Imprecision, Heterogeneity, Incoherence. Overall confidence: High / Moderate / Low / Very Low. Based on computable criteria from the NMA results.

Direct vs Network Estimates (Split Forest)

For each comparison with direct evidence, shows three estimates: Direct (pairwise MA of head-to-head studies), Network (NMA consistency model), and Indirect (derived). Agreement supports consistency. Disagreement flags potential incoherence.

Network Forest Plot — All T(T-1)/2 Pairwise Comparisons

Forest plot showing ALL pairwise NMA comparisons (not just vs reference). Grouped by comparison, sorted by effect size. Diamond = NMA estimate with 95% CI bars.

Treatment Effect Surface

2D visualization: X = effect vs reference, Y = precision (1/SE). Each treatment is a labeled point with approximate 95% confidence ellipses. Helps visualize which treatments cluster together and which are most precisely estimated.

Bayesian NMA (Monte Carlo Approximation)

Simplified Bayesian NMA using Monte Carlo sampling (5000 draws) with uninformative priors: Normal(0, 100) for treatment effects, Half-Normal(0, 1) for tau. Posterior medians with 95% CrI. Seeded PRNG for reproducibility. Compare with frequentist estimates below.

Comparison	Posterior Median	95% CrI	Frequentist Est	Freq 95% CI	Agreement

Bayesian vs Frequentist Comparison

Transitivity Assessment

Transitivity is the fundamental assumption of NMA: study populations across comparisons must be sufficiently similar. This table compares study-level characteristics (sample size proxy, precision, study count) across direct comparisons to flag potential violations.

Network Connectivity & Vulnerability

Identifies bridge edges (single points of failure): direct comparisons whose removal would disconnect the network. Bridge edges are critical — the entire NMA depends on them for indirect evidence flow.

Network Meta-Regression (Covariate Adjustment)

Extends the NMA model with a study-level covariate: Y = X*beta + Z*gamma + epsilon. The covariate is centered at its mean. Reports the covariate effect (gamma) and proportion of heterogeneity explained. If no covariate column is present in the data, a precision-based proxy (1/SE, centered) is used as a demonstration.

Network Meta-Analysis — Guide

NMA synthesizes evidence from a network of treatments, combining direct comparisons (head-to-head trials) with indirect evidence (via common comparators). Key assumption: transitivity (patient populations are similar across trials).

Consistency	Direct and indirect evidence should agree. Tested globally (Q decomposition) and locally (node-splitting).
P-score	Frequentist analogue of SUCRA. Ranges 0-1; higher = more likely to be best. Should be reported alongside effect estimates, not used alone for ranking.
League table	Matrix of all pairwise comparisons. Read as row vs column. Colored by significance.
Prediction Interval	Shows where the true effect in a new study setting might fall. Uses t-distribution with df = k_designs - T + 1 and adds tau-squared to the variance.
Net Heat Plot	Matrix heatmap showing how each design (direct comparison) contributes to each NMA estimate. Warm colors = high contribution. Red borders = inconsistency hotspots (Krahn et al. 2013, BMC Med Res Meth).
Contribution Matrix	Percentage table: how much each direct comparison drives each NMA estimate. Based on the hat matrix approach (Papakonstantinou et al. 2018, Stat Med).
SIDE Test	Separating Indirect from Direct Evidence. Proper node-splitting test (Koenig et al. 2013): z-test comparing direct and indirect estimates.
Comparison-Adjusted Funnel	Residuals (study effect minus NMA estimate) plotted against SE. Asymmetry suggests small-study effects (Chaimani & Salanti 2012).
CINeMA	Confidence in NMA estimates across 6 domains: within-study bias, reporting bias, indirectness, imprecision, heterogeneity, incoherence (Nikolakopoulou et al. 2020).
Rank Robustness	Leave-one-out stability: what proportion of study removals preserve the ranking order for each treatment pair.
Design-by-Treatment	Global inconsistency test (Higgins et al. 2012): decomposes Q into heterogeneity and inconsistency components. Omnibus test complementing local node-splitting.
Rankogram	Proper simulation-based rankogram (Salanti et al. 2011): 1000 MVN samples from (beta, vcov), computing rank probabilities as heatmap. Reports mean rank and 95% CrI.
SUCRA	Surface Under Cumulative Ranking: SUCRA_i = sum(P(rank ≤ r)) / (T-1). Frequentist analogue should closely match P-scores. Computed from rankogram simulations.
Small-Study Effects	Comparison-adjusted Egger-like regression (Chaimani & Salanti 2012): tests slope of residuals vs SE. Adapted for NMA with comparison indicators.
Transitivity	Assessment table comparing study characteristics (precision, count, year proxy) across direct comparisons to check the fundamental NMA assumption.
Direct vs NMA	Split forest plot showing direct, network, and indirect estimates side-by-side for each comparison with head-to-head evidence.
Bridge Edges	Network vulnerability: identifies edges whose removal disconnects the network. Critical comparisons that the entire indirect evidence chain depends on.
Living NMA	Add new trials and re-analyze to track how network estimates evolve over time.
Pairwise MA	Standard pairwise random-effects MA for each direct comparison with 2+ studies. Reports pooled direct estimate, CI, I-squared, tau-squared, and compares with NMA estimate.
Het Decomposition	Compares common tau-squared model with comparison-specific tau-squared. Flags comparisons with tau-squared exceeding 2x the common value.
Information Fraction	For each NMA estimate, computes the percentage of information from direct vs indirect evidence. Stacked bar chart visualization. Flags comparisons with less than 20% direct evidence.
Network Meta-Regression	Extends NMA with a study-level covariate. Reports covariate effect and proportion of heterogeneity explained. Useful for assessing treatment effect modification.
Bayesian NMA	Monte Carlo approximation with Normal(0,100) priors for effects and Half-Normal(0,1) for tau. 5000 draws with seeded PRNG. Compares posterior medians and CrI with frequentist estimates.
All Pairs Forest	Forest plot of all T(T-1)/2 pairwise NMA comparisons, sorted by effect size. Shows diamonds and CI bars for every comparison.
Effect Surface	2D scatter of treatments: effect vs reference on X, precision on Y. Confidence ellipses show estimation uncertainty. Visualizes treatment clustering.