Development of Variance Formulae for Optimally Weighted Studies in Meta-Analyses with Continuous Outcomes

Abstract

A meta-analysis provides a convenient way to integrate findings from multiple studies. The conventional methods of conducting a meta-analysis use inverse sample variance as weights, which are biased. However, this bias can easily be remedied using a multiplicative correction factor under a fixed-effects model, when the outcome is continuous and the treatment groups share a common variance. To investigate the effects of the bias correction, Taylor series approximation is used to derive new estimators for the variance of the summary treatment effect. Results obtained from a simulation study show that the Taylor-approximated estimators return superior coverage with near-maximum precision. The bias-correction leads to increased coverage in some cases, although the results are inconclusive. The conventional inverse sum-of-weights estimator for the summary effect variance always underestimates the variance, decreasing the coverage. The work here demonstrates how the bias-correction impacts the precision of the overall treatment effect estimate and provides improved estimators for the variance, with which confidence intervals can be constructed, for example.