Network meta-analysis
Plots for connected networks of randomized comparisons
Network meta-analysis combines direct and indirect evidence across a connected network of treatments. On top of the pairwise questions it adds three more: how the network is built, whether direct and indirect evidence agree, and how treatments rank. Rankings should never replace the relative effects and their uncertainty.
Minimum graphical set
- A network graph and a transitivity plot of key effect modifiers.
- Relative effects as an NMA forest plot, league table, or interval plot.
- An inconsistency diagnostic: node-splitting forest, net heat plot, or dev-dev plot.
- A contribution matrix or evidence flow when the provenance of estimates matters, as in CINeMA.
- Rankings, if reported, as full distributions (rankogram or cumulative ranking) next to the effect estimates.
All plots for network meta-analysis
Effect display
Estimates, intervals, and pooled summaries: the forest plot and its many descendants.
Forest plot
Study estimates and confidence intervals on a common effect scale, with the pooled estimate drawn as a diamond.
Prediction interval plot
Contrasts the confidence interval for the average effect with the prediction interval for the effect in a new setting.
Subgroup forest plot
A forest plot split by a categorical moderator, with a pooled estimate per subgroup and a test for subgroup differences.
Bayesian shrinkage forest plot
Observed study estimates next to their Bayesian shrinkage estimates, which borrow strength from the other studies.
Meta-regression bubble plot
Study effects against a continuous moderator, with bubbles sized by precision and a fitted meta-regression line.
NMA forest plot
Network estimates of every treatment against one reference, with the number of direct trials and a ranking score.
NMA interval plot
Every pairwise network estimate with its confidence and prediction interval on one axis.
League table heat plot
All pairwise network estimates arranged in a treatment-by-treatment matrix and colored by the size and direction of the effect.
Heterogeneity and influence
Where between-study variation comes from, and which studies move the pooled result.
Radial plot
Standardized effects against precision; the slope of a line through the origin is the pooled estimate, and studies far from it are heterogeneous.
Leave-one-out forest plot
The pooled estimate recomputed after omitting each study in turn, with the resulting heterogeneity.
Heterogeneity profile likelihood plot
The restricted log-likelihood across values of the between-study variance, showing its estimate, uncertainty, and whether it is well identified.
Small-study effects and reporting bias
Funnel plots and their successors for exploring asymmetry, selective reporting, and sensitivity to it.
Model checking and Bayesian diagnostics
Residuals, fit, predictive checks, and the computational health of Bayesian models.
Residual versus fitted plot
Standardized residuals against fitted values from a meta-regression or outcome model, to detect misspecification and outliers.
Normal Q-Q plot
Standardized residuals against normal quantiles, with a simulated envelope, to check the normality assumption of the random-effects model.
Leverage versus residual deviance plot
Each data point's leverage against its signed Bayesian deviance residual, with contours of its contribution to the DIC.
Residual deviance plot
The posterior residual deviance of every data point, which should be about 1 under good fit.
Observed versus predicted plot
Observed arm-level or study-level outcomes against model predictions, around the line of perfect agreement.
Posterior predictive check
Observed data against data replicated from the fitted Bayesian model, to check whether the model can reproduce what was seen.
MCMC trace, rank, and density plots
Sampled values by iteration, rank histograms by chain, and per-chain densities, to check that Markov chains have converged and mixed.
Prior versus posterior plot
Prior densities overlaid on posterior distributions, showing how much the data updated each parameter.
Posterior predictive distribution plot
The posterior of the mean effect next to the posterior predictive distribution of the true effect in a new study.
Network geometry and evidence flow
Which treatments are compared directly, how much evidence each comparison carries, and where it flows.
Network graph
Treatments as nodes and direct randomized comparisons as edges, showing how the evidence base is connected.
Transitivity plot
The distribution of potential effect modifiers across trials or direct comparisons, to judge whether indirect comparisons are plausible.
Evidence flow diagram
For one network estimate, arrows show how much evidence flows through each direct comparison, exposing the indirect paths behind the result.
Contribution matrix
The percentage of each network estimate that comes from each direct comparison, drawn as a heat map.
Direct evidence plot
For each comparison, the proportion of direct evidence, the mean length of the paths that contribute, and the minimal parallelism.
Inconsistency
Agreement between direct and indirect evidence, locally and across the whole network.
Net heat plot
A matrix showing how much each design contributes to each network estimate and how inconsistency changes when that design is detached.
Node-splitting forest plot
Direct, indirect, and network estimates for every comparison informed by both kinds of evidence, stacked as forest-plot rows.
Local inconsistency scatter plot
The difference between direct and indirect estimates against the network estimate for every split comparison, with confidence intervals.
Loop inconsistency plot
The inconsistency factor of every closed loop in the network, with confidence intervals truncated at zero.
Dev-dev plot
Each data point's residual deviance under the consistency model against the unrelated mean effects model.
Q decomposition plot
Cochran's Q split into within-design heterogeneity and between-design inconsistency, with the contribution of each design.
Path-based inconsistency heat plot
Pairwise standardized differences between the estimates of one comparison obtained through each independent path in the network.
Bayesian node-split density plot
For each split comparison, the posterior distributions of the direct, indirect, and network estimates from Bayesian node-splitting models.
Treatment ranking
Rank probabilities and their summaries. Always read them next to the effect estimates.
Rankogram
For each treatment, the probability of occupying each rank from best to worst.
Cumulative ranking plot
The probability of each treatment being at or better than each rank; the area under each curve is its SUCRA.
P-score plot
P-scores (or SUCRA values) for each treatment across several outcomes, arranged as a colored matrix.
Rank probability heat map
A matrix of treatments by ranks, colored by the probability of each rank.
Rank-heat plot
Concentric rings for outcomes and sectors for treatments, colored by ranking score.
Multidimensional scaling ranking plot
Treatments placed along a dimension recovered by multidimensional scaling of the pairwise effect matrix.
Hasse diagram
Treatments ordered only where one is better than another on every outcome, avoiding a forced single ranking.
Clustered ranking plot
Ranking scores for two outcomes plotted against each other, with treatments grouped by hierarchical clustering.
Litmus Rank-O-Gram
Cumulative rank curves colored by SUCRA, paired with a vertical color strip that places each treatment on the SUCRA scale.
Radial SUCRA plot
Treatments placed at a radius equal to their SUCRA, with the network's direct comparisons drawn between them.
Beading plot
One horizontal thread per outcome, with each treatment as a colored bead positioned at its ranking score.
Spie chart
One chart per treatment with equal-angle sectors for outcomes and sector radius proportional to the ranking score.
Kilim plot
A table of treatments by outcomes showing absolute effects, with cell colors for the strength and direction of evidence.
Vitruvian plot
Small multiple circular bar charts, one per treatment, showing absolute outcome rates colored by evidence against the reference.
Component, dose-response, and threshold NMA
Extensions of NMA for complex interventions, dose-response relationships, and decision robustness.
Component NMA forest plot
Effects of complex interventions estimated from an additive component network meta-analysis, where each intervention's effect is the sum of its components.
Component heat plot
A matrix of pairs of components, each cell summarizing the relative effects of interventions that contain both.
Dose-response NMA plot
Fitted dose-response curves for several agents from a model-based network meta-analysis.
Threshold analysis forest plot
For each study estimate, how far it could change before the treatment recommendation changes, shown as an invariant interval next to the 95% CI.
Multilevel network meta-regression
ML-NMR graphics for mixed IPD and aggregate networks, numerical integration, and population-specific effects.
Mixed IPD and aggregate-data network plot
A network graph that distinguishes comparisons informed by individual patient data from those informed by aggregate data.
Predicted absolute outcomes by population
Predicted probability of the outcome on each treatment in each study population, including the reference treatment.
Network meta-interpolation
NMI graphics built on subgroup evidence and interpolation to a common effect-modifier value.
Survival and time-to-event
Kaplan-Meier displays, proportional hazards checks, and time-varying effects across ITC methods.
Fitted survival curves with Kaplan-Meier overlay
Survival curves predicted by a parametric NMA or ML-NMR model, overlaid on each study's observed Kaplan-Meier curves.
Proportional hazards diagnostic plots
Log cumulative hazard against log time and scaled Schoenfeld residuals over time, before and after weighting, to check proportional hazards.
Time-varying hazard ratio plot
The hazard ratio as a function of time from a flexible survival model, compared with the constant hazard ratio from a Cox model.
Kaplan-Meier reconstruction check
A published Kaplan-Meier curve overlaid with the curve rebuilt from reconstructed pseudo-IPD, to validate the reconstruction.
Risk of bias and reporting
Study-level quality displays that accompany the quantitative synthesis.
Simulation and method evaluation
Graphics from the proof-of-concept literature that evaluates methods under known truth.
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