Variable selection in linear mixed model meta-regression with suspected interaction effects -- How can tree-based methods help?

TL;DR

This study compares linear and tree-based methods for detecting interaction effects in meta-regression, highlighting the robustness of tree-based approaches, especially stability-selected random effects trees, in various data scenarios.

Contribution

It provides a comprehensive evaluation of traditional linear and novel tree-based methods for variable selection in meta-regression with interaction effects, including stability-selected ensemble variants.

Findings

Linear methods excel with strictly linear interactions.

Tree-based methods are more conservative with small sample sizes.

Stability-selected trees perform well with larger samples and nonlinear interactions.

Abstract

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 fixed effect and random effects trees and their stability-selected ensemble variants. All methods are evaluated using a real-world meta-analytic dataset and a plasmode simulation study. The data-generating process assumes linear IEs and is complemented by settings with nonlinear 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, even in simple ways, the performance of linear methods deteriorates, whereas tree-based approaches, especially stability-selected fixed effect trees, provide a more robust alternative. Overall, stability-selected random effects trees are useful complementary tools for IE detection in applied meta-regression, particularly for metric covariates. They are well suited for pre-selection and sensitivity analyses, and selection frequency patterns in tree ensembles can help reveal structural patterns in the data.