A method for allocating evidence in meta-analyses

Article type
Goodman SN
Introduction: Even though meta-analytic methods are often described as a means to combine evidence from multiple studies, standard meta-analytic methods contain no formal measure of this evidence. Most standard methods can be re-interpreted as a sum of log-likelihood curves (Goodman, CCT, 1989), the log-likelihood ratio being a natural measure of evidence - a linear function of both the observed effect and of the sample size. Likelihood-based equations allow us to combine each trials observed effect size and precision to calculate what proportion of the total evidence for or against the pooled effect is provided by each individual trial. They can be used together with standard methods. Nontechnical audiences find proportional allocation of evidence intuitive and easy to understand.

Discussion: The proposed method uses simple algebraic equations and is easy to implement by non-statisticians. It lends itself to graphics with standard software which display how each trial contributes to the "weight of the evidence." It also has the nice theoretical feature of being interpretable in both frequentist and Bayesian frameworks, and being well suited to show the effects of random-effects modelling, quality-based weighting, or Bayesian priors. The features and limitations of this approach will be discussed, using recent meta-analyses from the literature.