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.

Meta-CART: A tool to identify interactions between moderators in meta-analysis

In the framework of meta-analysis, moderator analysis is usually performed only univariately. When several study characteristics are available that may account for treatment effect, standard meta-regression has difficulties in identifying interactions between them. To overcome this problem, meta-CART has been 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 previous version of meta-CART has its shortcomings: when applying CART, the sample sizes of studies are not taken into account, and the effect sizes are dichotomized around the median value. Therefore, this article proposes new meta-CART extensions, weighting study effect sizes by their accuracy, and using a regression tree to avoid dichotomization. In addition, new pruning rules are proposed. The performance of all versions of meta-CART was evaluated via a Monte Carlo simulation study. The simulation results revealed that meta-regression trees with random-effects weights and a 0.5-standard-error pruning rule perform best. The required sample size for meta-CART to achieve satisfactory performance depends on the number of study characteristics, the magnitude of the interactions, and the residual heterogeneity.