Causal rule ensemble approach for multi-arm data

TL;DR

The paper tackles multi-arm heterogeneous treatment effect estimation with a strong emphasis on interpretability. It extends RuleFit into a multi-arm setting by sharing a common set of base functions (rules and winsorized linear terms) across treatment arms and applying group-wise regularization to estimate HTE differences, Δ^(t)(x). Through extensive simulations and a real-world ACTG175 AIDS trial application, the method demonstrates competitive accuracy relative to black-box meta-learners while delivering clear, rule-based explanations of how covariates drive treatment effects. The approach facilitates per-patient treatment decisions and comparative interpretation across arms, highlighting key covariates such as baseline CD4, baseline CD8, and weight as influential factors. Overall, it offers a principled balance between predictive performance and interpretability, contributing a practical tool for precision medicine in multi-arm contexts.

Abstract

Heterogeneous treatment effect (HTE) estimation is critical in medical research. It provides insights into how treatment effects vary among individuals, which can provide statistical evidence for precision medicine. While most existing methods focus on binary treatment situations, real-world applications often involve multiple interventions. However, current HTE estimation methods are primarily designed for binary comparisons and often rely on black-box models, which limit their applicability and interpretability in multi-arm settings. To address these challenges, we propose an interpretable machine learning framework for HTE estimation in multi-arm trials. Our method employs a rule-based ensemble approach consisting of rule generation, rule ensemble, and HTE estimation, ensuring both predictive accuracy and interpretability. Through extensive simulation studies and real data applications, the performance of our method was evaluated against state-of-the-art multi-arm HTE estimation approaches. The results indicate that our approach achieved lower bias and higher estimation accuracy compared with those of existing methods. Furthermore, the interpretability of our framework allows clearer insights into how covariates influence treatment effects, facilitating clinical decision making. By bridging the gap between accuracy and interpretability, our study contributes a valuable tool for multi-arm HTE estimation, supporting precision medicine.

Figures (10)

• Figure 1: Brief procedure of proposed approach.
• Figure 2: Results of mean mPEHE across twelve scenarios for all approaches. The plots in the first column illustrate the performance of meta-learners using BART under both RCT (left) and observational settings (right). In each plot, the $x$-axis represents the number of treatment groups while the $y$-axis denotes the mPEHE. These line charts depict the mean mPEHE along with their standard deviations, represented by error bars.
• Figure 3: Results in terms of the mean absolute relative bias across twelve scenarios for all approaches. In each plot, the x-axis represents the number of treatment groups, while the $y$-axis denotes the mean absolute relative bias across. These line charts depict the average of mean absolute relative bias along with their standard deviations, represented by error bars.
• Figure 4: Results in terms of mean Cohen's kappa across twelve scenarios for all approaches. The plots in the first column illustrate the performance of meta-learners using BART under both RCT (rct) and observational (obv) settings, whereas the plots in the second column display the results of the proposed approach in the same settings. In each plot, the x-axis represents the number of treatment groups, while the y-axis denotes the Spearman’s rank correlation. These line charts depict the mean Cohen's kappa along with their standard deviations, represented by error bars.
• Figure 5: Results in terms of mean Spearman’s rank correlation across twelve scenarios for all approaches are presented. The plots in the first column illustrate the performance of meta-learners using BART under both RCT (rct) and observational (obv) settings, whereas the plots in the second column display the results of the proposed approach in the same settings. In each plot, the x-axis represents the number of treatment groups while the y-axis denotes the Spearman’s rank correlation. These line charts depict the mean Spearman’s rank correlation along with their standard deviations, represented by error bars.