Empirical vs natural weighting in random effects meta-analysis.

This article brings into serious question the validity of empirically based weighting in random effects meta-analysis. These methods treat sample sizes as non-random, whereas they need to be part of the random effects analysis. It will be demonstrated that empirical weighting risks substantial bias. Two alternate methods are proposed. The first estimates the arithmetic mean of the population of study effect sizes per the classical model for random effects meta-analysis. We show that anything other than an unweighted mean of study effect sizes will risk serious bias for this targeted parameter. The second method estimates a patient level effect size, something quite different from the first. To prevent inconsistent estimation for this population parameter, the study effect sizes must be weighted in proportion to their total sample sizes for the trial. The two approaches will be presented for a meta-analysis of a nasal decongestant, while at the same time will produce counter-intuitive results for the DerSimonian-Laird approach, the most popular empirically based weighted method. It is concluded that all past publications based on empirically weighted random effects meta-analysis should be revisited to see if the qualitative conclusions hold up under the methods proposed herein. It is also recommended that empirically based weighted random effects meta-analysis not be used in the future, unless strong cautions about the assumptions underlying these analyses are stated, and at a minimum, some form of secondary analysis based on the principles set forth in this article be provided to supplement the primary analysis.