Abstract
We outline a Bayesian model‐averaged (BMA) meta‐analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness δ and across‐study heterogeneity τ. We construct four competing models by orthogonally combining two present‐absent assumptions, one for the treatment effect and one for across‐study heterogeneity. To inform the choice of prior distributions for the model parameters, we used 50% of the Cochrane Database of Systematic Reviews to specify rival prior distributions for δ and τ. The relative predictive performance of the competing models and rival prior distributions was assessed using the remaining 50% of the Cochrane Database. On average, ℋ1r—the model that assumes the presence of a treatment effect as well as across‐study heterogeneity—outpredicted the other models, but not by a large margin. Within ℋ1r, predictive adequacy was relatively constant across the rival prior distributions. We propose specific empirical prior distributions, both for the field in general and for each of 46 specific medical subdisciplines. An example from oral health demonstrates how the proposed prior distributions can be used to conduct a BMA meta‐analysis in the open‐source software R and JASP. The preregistered analysis plan is available at https://osf.io/zs3df/.
Highlights
Following Karl Pearson’s first quantitative synthesis of clinical trials in 1904, meta-analysis gradually established itself as an irreplaceable method for statistics in medicine.[1]
Developed in the second half of the 1930s by Sir Harold Jeffreys,[12,13] the Bayesian testing framework seeks to grade the evidence that the data provide for or against a specific value of interest such as δ = 0 and τ = 0 which corresponds to the null model of no effect and the fixed-effect model, respectively
We developed and assessed prior distributions for the δ and τ parameters suitable for Bayesian model-averaged (BMA) of continuous outcomes using data from Cochrane Database of Systematic Reviews (CDSR).¶ In the remainder of this work, we adopt the terminology of Higgins et al[49]: individual meta-analyses included in each Cochrane review are referred to as “comparisons” and individual studies included in a comparison are referred to as “studies.” All of the results were conducted using Cohen’s d standardized mean differences (SMD)
Summary
Following Karl Pearson’s first quantitative synthesis of clinical trials in 1904, meta-analysis gradually established itself as an irreplaceable method for statistics in medicine.[1]. In contrast to this work, here we seek to construct and compare different prior distributions based on existing medical knowledge.[25,26,27] we propose empirical prior distributions for δ and τ as applied to meta-analyses of continuous outcomes in medicine. To this aim, we first used 50% of CDSR to develop candidate prior distributions and used the remaining 50% of CDSR to evaluate their predictive accuracy and that of the associated models. We demonstrate with a concrete example how our results can be applied in practice using the open-source statistical programs R28 and JASP.[29]
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