Edgington's Method for Random-Effects Meta-Analysis Part II: Prediction

Statistical inference about the average effect in random-effects meta-analysis has been considered insufficient in the presence of substantial between-study heterogeneity. Predictive distributions are well-suited for quantifying heterogeneity since they are interpretable on the effect scale and provide clinically relevant information about future events. We construct predictive distributions accounting for uncertainty through confidence distributions from Edgington's $p$-value combination method and the generalized heterogeneity statistic. Simulation results suggest that 95% prediction intervals typically achieve nominal coverage when more than three studies are available and effectively reflect skewness in effect estimates in scenarios with 20 or less studies. Formulations that ignore uncertainty in heterogeneity estimation typically fail to achieve correct coverage, underscoring the need for this adjustment in random-effects meta-analysis.