A flexible approach to identify interaction effects between moderators in meta‐analysis

In meta‐analytic studies, there are often multiple moderators available (eg, study characteristics). In such cases, traditional meta‐analysis methods often lack sufficient power to investigate interaction effects between moderators, especially high‐order interactions. To overcome this problem, meta‐CART was proposed: an approach that applies classification and regression trees (CART) to identify interactions, and then subgroup meta‐analysis to test the significance of moderator effects. The aim of this study is to improve meta‐CART upon two aspects: 1) to integrate the two steps of the approach into one and 2) to consistently take into account the fixed‐effect or random‐effects assumption in both the the interaction identification and testing process. For fixed effect meta‐CART, weights are applied, and subgroup analysis is adapted. For random effects meta‐CART, a new algorithm has been developed. The performance of the improved meta‐CART was investigated via an extensive simulation study on different types of moderator variables (ie, dichotomous, nominal, ordinal, and continuous variables). The simulation results revealed that the new method can achieve satisfactory performance (power greater than 0.80 and Type I error less than 0.05) if appropriate pruning rule is applied and the number of studies is large enough. The required minimum number of studies ranges from 40 to 120 depending on the complexity and strength of the interaction effects, the within‐study sample size, the type of moderators, and the residual heterogeneity.