Pairwise meta-analysis
Plots for aggregate-data and IPD pairwise meta-analysis
Pairwise meta-analysis combines randomized comparisons of the same two treatments. Its graphics answer four questions: what the effects are, how much they vary, which studies drive the result, and whether small studies behave differently from large ones. A result plot should always be paired with a plot of the assumption or data structure that makes it credible.
Minimum graphical set
- A forest plot with a prediction interval when a random-effects model is used.
- A heterogeneity or influence diagnostic: Baujat plot, leave-one-out forest, or influence panel.
- A funnel plot, preferably contour-enhanced, only when there are enough studies (about ten or more).
- A bubble plot or subgroup forest plot whenever heterogeneity is being explained.
All plots for pairwise 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.
Cumulative meta-analysis plot
Pooled estimate recomputed as each study is added in a chosen order, showing how the evidence evolved.
Trial sequential analysis plot
Cumulative z-statistic plotted against accrued information, with alpha-spending boundaries and the required information size.
Rainforest plot
A forest plot variant in which each confidence interval is drawn as a likelihood-shaped drop, so that precision and plausibility are visible.
Thick forest plot
A forest plot in which each confidence interval is drawn as a bar whose thickness reflects study weight.
Caterpillar plot
Every effect size sorted by magnitude with its confidence interval, plus the overall mean and prediction interval.
Orchard plot
Pooled estimates, confidence intervals, and prediction intervals per moderator level, drawn over a swarm of the individual effect sizes.
Drapery plot
p-value functions for each study and the pooled estimate, showing evidence across all confidence levels instead of one 95% cutoff.
Bayesian shrinkage forest plot
Observed study estimates next to their Bayesian shrinkage estimates, which borrow strength from the other studies.
L'Abbé plot
Event risk in the treatment arm against event risk in the control arm, one point per study, around the line of equality.
Meta-regression bubble plot
Study effects against a continuous moderator, with bubbles sized by precision and a fitted meta-regression line.
Meta-plot
Study effects against precision, a cumulative meta-analysis from most to least precise study, and each study's power to detect small, medium, and large effects.
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.
Baujat plot
Each study's contribution to overall heterogeneity against its influence on the pooled estimate.
GOSH plot
Pooled estimate against heterogeneity for every subset of studies, revealing clusters that point to influential studies or latent subgroups.
Leave-one-out forest plot
The pooled estimate recomputed after omitting each study in turn, with the resulting heterogeneity.
Influence diagnostics panel
Eight case-deletion statistics per study, including studentized residuals, Cook's distance, DFFITS, and hat values, with cutoffs.
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.
Funnel plot
Study effects against their standard errors; asymmetry suggests small-study effects, of which publication bias is one possible cause.
Contour-enhanced funnel plot
A funnel plot overlaid with regions of statistical significance, to judge whether missing studies fall where non-significant results would be.
Trim-and-fill funnel plot
A funnel plot with algorithmically imputed "missing" studies that would make it symmetric, and the adjusted pooled estimate.
Sunset funnel plot
A funnel plot whose background shows the statistical power of a study at each level of precision to detect an assumed true effect.
Doi plot
Effect estimates against the absolute z-score in a folded normal quantile display, summarized by the LFK asymmetry index.
PET-PEESE plot
Study effects against standard error with weighted regression lines whose intercepts estimate the effect in a study of infinite precision.
Selection model weight function plot
The estimated relative probability that a study is published as a function of its p-value, from a selection model.
Copas selection model plot
A four-panel sensitivity analysis showing how the pooled estimate changes as the assumed probability of publishing small studies falls.
Limit meta-analysis funnel plot
A funnel plot showing each study's estimate shrunk to what an infinitely precise version of it would give, with the limit meta-analysis curve.
p-curve plot
The distribution of statistically significant p-values, compared with the shapes expected under no effect and under low power.
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.
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.
Joint posterior plot of effect and heterogeneity
The joint posterior density of the mean effect and the between-study SD, with credible regions and the conditional mean.
Component, dose-response, and threshold NMA
Extensions of NMA for complex interventions, dose-response relationships, and decision robustness.
Survival and time-to-event
Kaplan-Meier displays, proportional hazards checks, and time-varying effects across ITC methods.
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.
Synthesis without meta-analysis
Graphics for reviews where effect sizes cannot be pooled.
Albatross plot
Studies placed by their p-value and direction against sample size, over contours of standardized effect size, for reviews without pooled effect sizes.
Harvest plot
One bar per study, grouped by outcome and direction of effect, with bar height and shading for study quality and design.
Effect direction plot
A study-by-outcome grid showing the direction of effect with arrows, sized by sample size.
Risk of bias and reporting
Study-level quality displays that accompany the quantitative synthesis.
Risk-of-bias traffic light plot
A grid of studies by risk-of-bias domains, with colored symbols for each judgment.
Risk-of-bias summary plot
Stacked bars showing the proportion of studies, or of statistical information, at each level of risk in each domain.
Forest plot with risk-of-bias columns
A forest plot with a traffic-light column for each risk-of-bias domain beside every study.
Simulation and method evaluation
Graphics from the proof-of-concept literature that evaluates methods under known truth.
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