Multilevel network meta-regression

Plots for ML-NMR with mixed IPD and aggregate data

ML-NMR (Phillippo and colleagues, 2020) extends network meta-regression by defining an individual-level model and integrating it over the covariate distribution of each aggregate-data study. It uses all IPD and aggregate data in a connected network, avoids aggregation bias, and produces effects in any specified target population. Its graphics add a numerical diagnostic that ordinary Bayesian checks miss: the integration error.

Minimum graphical set

All plots for ML-NMR

Effect display

Estimates, intervals, and pooled summaries: the forest plot and its many descendants.

Subgroup forest plot
A forest plot split by a categorical moderator, with a pooled estimate per subgroup and a test for subgroup differences.
MANMANMIML-NMR
NMA forest plot
Network estimates of every treatment against one reference, with the number of direct trials and a ranking score.
NMAML-NMR
Method-comparison forest plot
The same treatment comparison estimated by several indirect comparison methods, stacked as forest rows, often against a known truth.
ITCMAICSTCML-NMRNMIML-UMR

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.
MANMASTCML-NMRML-UMR
Leverage versus residual deviance plot
Each data point's leverage against its signed Bayesian deviance residual, with contours of its contribution to the DIC.
MANMAML-NMR
Residual deviance plot
The posterior residual deviance of every data point, which should be about 1 under good fit.
MANMAML-NMR
Observed versus predicted plot
Observed arm-level or study-level outcomes against model predictions, around the line of perfect agreement.
NMASTCML-NMRML-UMR
Posterior predictive check
Observed data against data replicated from the fitted Bayesian model, to check whether the model can reproduce what was seen.
MANMAML-NMRML-UMR
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.
MANMAML-NMRML-UMRSTC
Prior versus posterior plot
Prior densities overlaid on posterior distributions, showing how much the data updated each parameter.
MANMAML-NMRML-UMR

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.
NMAML-NMRNMI
Transitivity plot
The distribution of potential effect modifiers across trials or direct comparisons, to judge whether indirect comparisons are plausible.
NMAML-NMRNMIITC

Inconsistency

Agreement between direct and indirect evidence, locally and across the whole network.

Dev-dev plot
Each data point's residual deviance under the consistency model against the unrelated mean effects model.
NMAML-NMR

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.
NMAML-NMR
Cumulative ranking plot
The probability of each treatment being at or better than each rank; the area under each curve is its SUCRA.
NMAML-NMR
Rank probability heat map
A matrix of treatments by ranks, colored by the probability of each rank.
NMAML-NMR

Weighting, balance, and overlap

MAIC diagnostics: what the weights did, how much information survived, and whether populations overlap.

Love plot
Standardized differences between the IPD and the comparator population for each covariate, before and after weighting.
MAICSTCML-NMRNMIML-UMR
Trial-membership score overlap plot
Distributions of the estimated probability of belonging to one trial, drawn separately for each trial, to assess common support.
MAICSTCML-NMR
Multivariate support plot
IPD participants projected onto principal components with their convex hull, and target population means projected into the same space.
MAICSTCML-NMRML-UMR

Outcome regression and transportability

STC and G-computation diagnostics: functional form, extrapolation, and effects in a target population.

Outcome model partial effect plot
Predicted outcomes from an STC or G-computation outcome model across one covariate, for each treatment, with the observed covariate distribution and the target population marked.
STCML-NMRML-UMR
Marginal effect by target population
The marginal treatment effect standardized to several target populations, showing that with effect modification the effect is a property of the population.
STCML-NMRNMIML-UMR
Treatment effect response surface
The conditional treatment effect over a grid of two effect modifiers, with the observed data support overlaid.
STCML-NMRML-UMR
Conditional versus marginal effect plot
How the marginal odds ratio drifts away from a fixed conditional odds ratio as a prognostic covariate becomes stronger.
STCML-NMRML-UMRMAIC

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.
ML-NMRNMA
Integration error plot
The estimated error of the quasi-Monte Carlo integration over each aggregate study's covariate distribution, as the number of integration points grows.
ML-NMR
Effect-modifier curve
The conditional treatment effect against a covariate for each treatment, with the observed IPD and aggregate covariate values marked.
ML-NMRSTCNMIML-UMR
Population-specific relative effects
Population-average conditional relative effects against the reference for each treatment, in each study population of the network.
ML-NMR
Marginal effects by study population
Marginal treatment effects against the reference, averaged over the covariate distribution of each study population, for every treatment in the network.
ML-NMRML-UMRSTC
Predicted absolute outcomes by population
Predicted probability of the outcome on each treatment in each study population, including the reference treatment.
ML-NMRNMA

Network meta-interpolation

NMI graphics built on subgroup evidence and interpolation to a common effect-modifier value.

Effect-modification comparison plot
The treatment effect across values of an effect modifier as implied by each synthesis method, compared with the truth in a simulation.
NMIML-NMRNMA
Subgroup data availability matrix
A trial-by-subgroup grid showing which overall and subgroup-specific estimates are reported, and whether they come with standard errors.
NMIML-NMR

Unanchored multilevel meta-regression

ML-UMR graphics for disconnected evidence, where prognostic modeling carries the whole comparison.

Absolute outcome plot
Posterior predicted outcome on each treatment, standardized to the index and comparator populations, from an unanchored ML-UMR model.
ML-UMRSTCML-NMR
Assumption sensitivity plot
The same unanchored treatment effect under increasingly flexible assumptions and priors, stacked to show how much the answer depends on untestable choices.
ML-UMRMAICSTCML-NMR

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.
NMAML-NMRSTCMAICML-UMR
Kaplan-Meier reconstruction check
A published Kaplan-Meier curve overlaid with the curve rebuilt from reconstructed pseudo-IPD, to validate the reconstruction.
MAICSTCML-NMRML-UMRNMA

Simulation and method evaluation

Graphics from the proof-of-concept literature that evaluates methods under known truth.

Nested loop plot
Performance of several methods across every scenario of a factorial simulation study, with scenarios ordered in nested loops and their factor levels drawn underneath.
MAICSTCML-NMRNMIML-UMR
Simulation performance plot
A performance measure for each method and scenario of a simulation study, with Monte Carlo uncertainty intervals.
MANMAMAICSTCML-NMRNMIML-UMR
Zip plot
Every replication's confidence interval, ranked by how far its estimate lies from the truth, showing which intervals fail to cover.
MANMAMAICSTCML-NMRNMIML-UMR

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