Multilevel unanchored meta-regression

Plots for ML-UMR with disconnected evidence

ML-UMR (Chandler and colleagues, 2026) extends ML-NMR ideas to disconnected, unanchored comparisons: it jointly models individual and aggregate data and marginalizes over each study’s covariate distribution, but without a common comparator every prognostic factor and effect modifier must be modeled correctly. The mlumr R package implements shared-prognostic-factor (SPFA) and relaxed variants. Because the method is new, there is no single established ML-UMR plot; the graphics below make absolute predictions and assumption dependence explicit.

Minimum graphical set

All plots for ML-UMR

Effect display

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

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
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

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
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.

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
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

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
Prognostic factor curve
Predicted outcomes on each treatment across a prognostic factor, showing where the unanchored model is supported by data and where it is not.
ML-UMRSTC
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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