Meta-analysis

Learn aboutmeta-analysis.

Seewhat's new in meta-analysis.

WatchMeta-analysis in Stata.

Data setup and effect sizes

• Effect sizes for two-sample binary data
• Odds ratio
• Peto's odds ratio
• Risk ratio
• Risk difference
• Effect sizes for two-sample continuous data
• Hedges's g
• Cohen's d
• Glass's delta (two versions)
• Unstandardized mean difference
• Effect sizes for one-sample binary data (prevalence data)New
  • Freeman–Tukey-transformed proportion
  • Logit-transformed proportion
  • Raw proportion
• Effect sizes for correlation dataStataNow
  • Fisher's \(z\)-transformed correlation
  • Raw correlation
• 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 summaryStataNow

• 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

Forest plotsStataNow

• Standard forest plot
• Custom forest plot
• Subgroup forest plot
• Cumulative forest plot
• Leave-one-out forest plot
• 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

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 asmargins,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

• 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 heterogeneity
  • Other standard postestimation tools such asmargins,contrasts, and more

Multilevel meta-regressionNew

• Multilevel meta-analysis
• Multilevel meta-regression with random slopes
• Estimation methods: REML and MLE
• Multilevel heterogeneity statistics
• Random-effects covariance structures
• Sensitivity analysis
• Postestimation features
• Fitted values
• Residuals
• Random effects
• Standard errors of predicted quantities
• Assess heterogeneity
• Other standard postestimation tools such asmargins,contrasts, and more.

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
• Perform multilevel meta-regression and pick from a variety of postestimation toolsNew

Additional resources

• Meta-Analysis Reference Manual, especially
• Introduction to meta-analysis
• Introduction to meta
• Meta-Analysis in Stata: An Updated Collection from the Stata Journal, Second Edition by Tom M. Palmer and Jonathan A. C. Sterne (editors)
• Meta-analysis flyer