A method was developed for correcting the bias in the usual study weights in meta-analyses

OBJECTIVES: Our goal was to evaluate the bias in the usual method of estimating study weights in a meta-analysis and to develop a suitable bias correction. STUDY DESIGN AND SETTING: In meta-analyses, it is standard practice to weight studies by the inverse variance of their treatment effects. Weights are usually calculated by taking reciprocals of the estimated variances, but we show that this approach is biased. We established an exact expression for the bias with continuous data, yielding a correction factor for the study weights that yields improved estimation of the treatment effect. RESULTS: With the usual method, the weight for each study is always overestimated, particularly with small samples; also, the variance of the summary treatment effect is underestimated. Our correction yields an unbiased estimate of the summary treatment effect with minimum variance. We illustrate the bias numerically for various scenarios and show how it can substantially affect actual meta-analyses in practice. CONCLUSION: We recommend that the standard method of obtaining study weights should be modified by our bias correction factor. Our method is simple and straightforward to apply. Elimination of this bias will enhance the validity of conclusions from a meta-analysis, compared with the situation when the standard weights are used.