Meta-analysis

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Meta-analysis

Combine results of multiple studies to estimate an overall effect. Use forest plots to visualize results. Evaluate study heterogeneity with subgroup analysis or meta-regression. Use funnel plots and formal tests to explore publication bias and small-study effects. Assess the impact of publication bias on results with trim-and-fill analysis. Perform cumulative meta-analysis. Use the meta suite of commands, or let the Control Panel interface guide you through your entire meta-analysis.

Learn about meta-analysis.

See what's new in meta-analysis.

Watch Meta-analysis in Stata.

Data setup and effect sizes

Effect sizes for binary data

Odds ratio
Peto's odds ratio
Risk ratio
Risk difference

Effect sizes for continuous data

Hedges's g
Cohen's d
Glass's delta (two versions)
Unstandardized mean difference

Generic (precomputed) effect sizes
Transformed effect sizes such as correlations and efficacies
Different methods for zero-cells adjustment with binary data
Update declared meta-analysis settings at any time
Describe declared meta-analysis settings

Meta-analysis models

Common-effect model

Inverse-variance method
Mantel–Haenszel method

Fixed-effects model

Inverse-variance method
Mantel–Haenszel method

Random-effects model

Iterative methods: REML, MLE, and empirical Bayes
Noniterative methods: DerSimonian–Laird, Hedges, Sidik–Jonkman, and Hunter–Schmidt
Knapp–Hartung standard-error adjustment
Prediction intervals
Sensitivity analysis: User-specified values for heterogeneity parameters tau2 and I2

Meta-analysis summary

Standard meta-analysis
Forest plots
Subgroup meta-analysis

One grouping variable
Multiple grouping variables
Subgroup forest plots

Cumulative meta-analysis

Standard analysis
Stratified analysis
Cumulative forest plots

Leave-one-out meta-analysis New

Watch Leave-one-out meta-analysis.

Forest plots

Standard forest plot
Custom forest plot
Subgroup forest plot
Cumulative forest plot
Leave-one-out forest plot New
Cropped CI ranges
Multiple overall effects

Heterogeneity

Basic summary
Forest plots
L'Abbé plots for binary data
Subgroup meta-analysis
Meta-regression
Bubble plots
Galbraith plots New

Watch Galbraith plots.

Meta-regression

Continuous and categorical moderators
Fixed-effects and random-effects regression
Multiplicative and additive residual heterogeneity
Knapp–Hartung standard-error adjustment
Postestimation features

Fitted values
Residuals
Random effects
Standard errors of predicted quantities
Bubble plots
Other standard postestimation tools such as margins, contrasts, and more

Small-study effects

Funnel plots
Tests for small-study effects

Funnel plots

Standard funnel plots
Contour-enhanced funnel plots
Two-sided or one-sided significance contours
Multiple precision metrics for the y-axis
Stratified funnel plots
Fully customizable

Tests for funnel-plot asymmetry or small-study effects

Egger regression-based test
Harbord regression-based test
Peters regression-based test
Begg rank correlation test
Adjust for moderators to account for heterogeneity
Traditional and random-effects versions

Publication bias

Funnel plots
Tests for funnel-plot assymetry
Nonparametric trim-and-fill method

Three estimators for number of missing studies
Impute studies on the left or right side of the funnel plot
Nine estimation methods for the iteration stage
Nine estimation methods for the pooling stage
Choose the side of the funnel plot with missing studies
Standard and contour-enhanced funnel plot for the observed and imputed studies

Multivariate meta-regression New

Multivariate meta-analysis
Fixed-effects and random-effects multivariate meta-regression
Estimation methods: REML, MLE, Jackson--White--Riley
Multivariate heterogeneity statistics
Jackson--Riley standard-error adjustment
Between-study covariance structures
Sensitivity analysis
Missing values
Postestimation features
- Fitted values
- Residuals
- Random effect
- Standard errors of predicted quantities
- Assess heterogenerity
- Other standard postestimation tools such as margins, contrasts, and more

Watch Multivariate meta-analysis.

Control panel

Set up data and compute effect sizes
Update specific characteristics at any time
Summarize results in tables and produce forest plots
Perform subgroup analysis and cumulative meta-analysis
Perform meta-regression and pick from a variety of postestimation tools
Perform publication bias analysis
Perform multivariate meta-regression and pick from a variety of postestimation tools