Incorporating Variation and Quality of the Underlying Effects in Meta-Analysis

This paper proposes a model to further explore the effects of the quality information and variation of the underlying effects on the summary effect measure in meta-analysis. A shape parameter is used in this model to quantify the asymmetry of the effect sizes of studies that are included. Estimation of the proposed model parameters is carried out by the Bayesian MCMC method. Performances of the resultant estimates are examined in the simulations and empirical case with data obtained from a total of 22 meta-analyses taken from three different designs. A conclusion would be drawn that it is advisable to take the proposed model, when quality information becomes available, in particular with a situation where the underlying effects approximately follow a normal distribution. If, however, the quality information is absent, the skew-normal distribution for random effect model should be adopted.