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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 x 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.