A random‐effects regression model for meta‐analysis

TLDR

Many meta‑analyses use a random‑effects model to account for heterogeneity among study results beyond the variation associated with fixed effects. The study proposes a random‑effects regression approach for 2×2 tables that incorporates covariates to explain heterogeneity and illustrates it by examining how a specific factor modifies vaccine efficacy. The method models 2×2 tables with covariates and extends to continuous outcomes, enabling heterogeneity explanation. Simulation studies show the random‑effects regression method yields low bias with a smoothed within‑study variance estimator, good power to detect overall efficacy, but limited power for weak covariates in small meta‑analyses.

Abstract

Abstract Many meta‐analyses use a random‐effects model to account for heterogeneity among study results, beyond the variation associated with fixed effects. A random‐effects regression approach for the synthesis of 2 × 2 tables allows the inclusion of covariates that may explain heterogeneity. A simulation study found that the random‐effects regression method performs well in the context of a meta‐analysis of the efficacy of a vaccine for the prevention of tuberculosis, where certain factors are thought to modify vaccine efficacy. A smoothed estimator of the within‐study variances produced less bias in the estimated regression coefficients. The method provided very good power for detecting a non‐zero intercept term (representing overall treatment efficacy) but low power for detecting a weak covariate in a meta‐analysis of 10 studies. We illustrate the model by exploring the relationship between vaccine efficacy and one factor thought to modify efficacy. The model also applies to the meta‐analysis of continuous outcomes when covariates are present.