Meta Regression
The Meta Regression section investigates whether study-level characteristics (covariates) explain heterogeneity in effect sizes. Where Subgroup Analysis splits studies into categorical groups, meta-regression models the relationship between the effect and one or more continuous or categorical covariates.
It answers questions like "Does the effect depend on mean participant age?" or "Is the effect larger in higher-quality studies?"
What you need
- Same per-study effect data as Main Analysis
- One or more covariates per study (e.g. mean age, year of publication, study quality score, dose, baseline risk)
Covariates can be continuous or categorical. The interface lets you mark each type and select which to include.
Supported effect measures
Mean Difference, Standardized Mean Difference, Paired Means, Single Mean, Risk Difference, Odds Ratio, Peto Odds Ratio, Risk Ratio, Hazard Ratio, Incidence Rate Ratio, Proportions/Prevalence, Correlation Coefficient, AUC-ROC, Diagnostic Test Accuracy, Generic Inverse Variance.
The workflow
| Step | What you do |
|---|---|
| 1. Select analysis type | Choose effect measure |
| 2. Enter study data | Add each study with effect data and covariate values |
| 3. Define covariates | Mark as continuous or categorical, select which to include |
| 4. Run regression | Engine fits model and returns coefficients, fit, adjusted effect |
Re-run with different covariate combinations to compare models.
What the regression reports
Per-covariate coefficients
| Field | Meaning |
|---|---|
| Coefficient | Change in effect size per unit increase in covariate |
| Standard error | SE of the coefficient |
| z-score | coefficient / SE |
| p-value | Two-tailed, from standard normal |
| 95% CI | coefficient +/- 1.96 * SE |
A small p-value indicates the covariate is associated with variation in effect size across studies.
Model summary
| Field | Meaning |
|---|---|
| Adjusted overall effect | Effect estimate after accounting for covariates |
| 95% CI | Confidence interval for adjusted estimate |
| Adjusted p-value | Significance of adjusted overall effect |
| Residual heterogeneity | Between-study variation not explained by covariates |
| R-squared | Proportion of between-study variance explained by covariates (%) |
High R-squared with a significant coefficient is the strongest evidence of a true effect modifier.
Estimation framework
Regression coefficients are estimated using the method of moments approach. Standard errors account for residual heterogeneity not explained by covariates. Hypothesis tests use Wald-type z-tests (p < 0.05, two-tailed).
Interpretation notes:
- Coefficients describe study-level associations, not causal claims
- Ecological inferences (individual-level conclusions from study-level data) require caution
- Conventional guidance: no more than one covariate per ten studies
Outputs
| Output | Contents |
|---|---|
| Coefficients table | Per-covariate coefficient, SE, z, p, 95% CI |
| R-squared | Percentage of heterogeneity explained |
| Residual heterogeneity | Remaining between-study variance |
| Adjusted overall effect | Point estimate and 95% CI |
| Model summary | Combined view |
| Bubble plot | Effect-covariate relationship (per continuous covariate) |
| Export | Coefficients and summary for manuscripts |
When to use Meta Regression vs Subgroup Analysis
| Question | Tool |
|---|---|
| Does the effect differ between categorical groups? | Subgroup Analysis |
| Does the effect change with a continuous covariate? | Meta Regression |
| Joint effect of multiple covariates? | Meta Regression |
| How much heterogeneity does a covariate explain? | Meta Regression (R-squared) |
The two are complementary: subgroup analysis for well-defined groups; meta-regression for flexible quantification of moderation.