Meta-Regression

Meta-regression is an extension of meta-analysis that uses study-level characteristics as explanatory variables to investigate why effect estimates differ across studies. Rather than reporting a single pooled value, it models the relationship between those characteristics and the size of the effect, attempting to explain between-study heterogeneity.

Definition

Meta-regression is a statistical technique that regresses the effect estimates from individual studies on one or more study-level covariates, usually within a random-effects framework, to assess how much of the between-study heterogeneity those covariates explain.

Scope

This entry covers meta-regression as a method within evidence synthesis: how study-level covariates are related to effect size, the random-effects (mixed) formulation that accounts for residual heterogeneity, and the well-known cautions about power, ecological bias, and over-interpretation. It is a reference description and not clinical guidance.

Core questions

• Which study-level characteristics are associated with larger or smaller effects?
• How much of the between-study heterogeneity does a covariate explain?
• Why is statistical power for meta-regression often low?
• When does a study-level association mislead about individual-level relationships?

Key concepts

• Study-level covariate
• Random-effects (mixed-effects) meta-regression
• Residual heterogeneity
• Ecological (aggregation) bias
• Multiplicity and over-fitting with few studies

Mechanisms

Each study supplies an effect estimate and a value of one or more study-level covariates, such as mean age, baseline risk, dose, or year of publication. Meta-regression fits a weighted regression of the effects on those covariates; because residual between-study variation usually remains, a random-effects (mixed-effects) formulation adds a residual heterogeneity term so that the covariate explains part, but rarely all, of the variation. Thompson and Sharp compared the available estimation methods, and Thompson and Higgins set out the practical principles: covariates should be pre-specified and few, because the number of studies is typically small and testing many covariates inflates false-positive findings. A central caution is ecological bias - an association between a study-average covariate and the study-average effect need not reflect the relationship within individuals, so meta-regression findings are hypothesis-generating rather than confirmatory.

Clinical relevance

Meta-regression can suggest which patient or study characteristics modify an intervention's effect, information that feeds cautiously into guidelines and health technology assessment, but its observational, study-level nature limits how strongly such findings can be acted on. This entry describes the method and is not a basis for individual treatment decisions.

Evidence & guidelines

The Cochrane Handbook (Higgins & Green, 2008) describes expected practice for meta-regression, including pre-specification of a small number of covariates and cautious interpretation, consistent with the methodological guidance of Thompson and Higgins (2002).

History

As meta-analysts increasingly confronted substantial heterogeneity in the 1990s, attention turned from merely measuring it to explaining it. Thompson and Sharp's 1999 comparison of methods and Thompson and Higgins's 2002 guidance established meta-regression's standard random-effects formulation and the interpretive cautions, particularly around power and ecological bias, that govern its use today.

Debates

How much weight should meta-regression findings carry?

Because meta-regression uses aggregate study-level data, often with few studies and multiple candidate covariates, its associations are prone to low power, confounding among study characteristics, and ecological bias, so commentators treat its results as hypothesis-generating rather than definitive.

Key figures

• Simon Thompson
• Julian Higgins
• Stephen Sharp

Seminal works

• thompson-sharp-1999
• thompson-higgins-2002

Frequently asked questions

How is meta-regression different from subgroup analysis?

Subgroup analysis splits studies into discrete categories and compares pooled effects between them, while meta-regression models the effect as a function of a covariate that can be continuous, using all studies together; subgroup analysis is in effect meta-regression with a categorical predictor.

Why is meta-regression often described as low-powered?

Because the unit of analysis is the study, and most meta-analyses contain relatively few studies, there is limited information to estimate covariate effects reliably, so non-significant results may simply reflect too few studies rather than a true absence of association.