Variable selection in linear mixed model meta-regression with suspected interaction effects -- How can tree-based methods help?
Detecting interaction effects (IEs) in meta-regression is challenging, especially when few studies are available and many plausible interactions are considered. In many meta-analyses, interpretability is essential, which limits the use of complex machine learning methods. Tree-based approaches offer a potentially useful compromise, but their role in meta-regression with random effects is not yet well understood. This paper examines how traditional linear and tree-based methods can support variable selection for IEs in random effects meta-regression. We compare test-based and information-criterion-based linear selection procedures with meta-CART approaches. These include single trees and tree ensembles, which combine single meta-CARTs into a stability selection ensemble based on bootstrapped data. All methods are evaluated using a real-world meta-analytic dataset and a simulation study. The data-generating process assumes linear IEs, complemented by settings with simple non-linear interactions. Our results show that under strictly linear interactions, linear selection methods perform as expected and achieve superior performance for IE detection. Tree-based methods are more conservative when the number of studies is small, but become competitive as sample size increases, particularly the stability-selected variants. When IEs deviate from strict linearity, Wald-type approaches can deteriorate, whereas criterion-based methods maintain a relatively stable performance. Tree-based methods, particularly stabilized versions of random-effects meta-CART, provide a robust alternative when a sufficient number of observations is available. They could thus be used for pre-selection and sensitivity analyses, guarding against more complex data structures. Additionally, selection frequency patterns from meta-CART tree ensembles can help to reveal structural patterns in the data in an exploratory way.