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Weighted mean or weighted mean difference

 

In meta-analysis, information to be pooled can either be dichotomous (how many patients dies, say, out of a total number), or continuous (the mean cholesterol was X mmol/L, with some estimate of variance).

For continuous variables we need to combine measures, where the mean, standard deviation and sample size in each group are known. The weight given to each study (how much influence each study has on the overall results of the meta-analysis) is determined by the precision of its estimate of effect and, in the statistical software in RevMan and CDSR, is equal to the inverse of the variance. This method assumes that all of the trials have measured the outcome on the same scale.

The weighted mean could be calculated for groups before and after an intervention (like blood pressure lowering), and the weighted mean difference would be the difference between start and finish values. For this, though, the difference would usually be calculated not as the difference between the overall start value and the overall final value, but rather as the sum of the differences in the individual studies, weighted by the individual variances for each study.

Precision is not the only way of calculating a weighted mean or weighted mean difference. Another, simpler, way is to weight by the number in the study. This is a defence against giving undue weight to small studies of low variance, where there may have been less than robust treatment of data, and where people could have cheated.