Metaregression

Metaregression, often called meta-regression, is a statistical method used in meta-analysis to examine whether study-level characteristics explain variation in treatment effects across studies. In metaregression, the dependent variable is the effect size estimate from each study (for example, log odds ratio, standardized mean difference, or risk ratio), and the independent variables are study-level covariates such as year of publication, sample size, dosing, population characteristics, or study design.

Typically, effect sizes are weighted by the inverse of their variance, and a regression model is fit to these weighted data. In a fixed-effects meta-regression, unexplained heterogeneity is attributed to sampling error, whereas a random-effects (or multilevel) meta-regression adds a term for residual between-study heterogeneity, often estimated by methods such as REML or DerSimonian-Laird. Univariate meta-regression includes one covariate; multivariate includes several.

Interpreting coefficients: a coefficient represents the expected change in the study effect size associated with a one-unit change in the covariate, holding other covariates constant. However, because meta-regression uses aggregate, study-level data, it is susceptible to ecological fallacy; associations at the study level may not reflect individual-level effects. Power is often limited, especially with few studies, leading to unstable estimates and potential false positives. Other limitations include measurement error in covariates, multicollinearity, selective reporting, and multiple testing.

Applications include exploring heterogeneity in clinical efficacy, adverse event rates, diagnostic performance, and epidemiological associations. Metaregression complements standard meta-analysis by identifying potential moderators and helping to explain variability in effects across studies.