[Paper Review] Random Forests of Interaction Trees for Estimating Individualized Treatment Effects in Randomized Trials

Xiaogang Su, Annette T. Peña+2 more|arXiv (Cornell University)|Sep 14, 2017

Advanced Causal Inference Techniques3 references3 citations

TL;DR

This paper proposes Random Forests of Interaction Trees (RFIT), a novel ensemble method that improves individualized treatment effect (ITE) estimation in randomized trials by using a smooth sigmoid surrogate (SSS) for faster tree construction and applying the infinitesimal jackknife to estimate standard errors. RFIT outperforms traditional separate regression by reducing bias and improving accuracy in ITE estimation, especially with small to moderate sample sizes.

ABSTRACT

Assessing heterogeneous treatment effects has become a growing interest in advancing precision medicine. Individualized treatment effects (ITE) play a critical role in such an endeavor. Concerning experimental data collected from randomized trials, we put forward a method, termed random forests of interaction trees (RFIT), for estimating ITE on the basis of interaction trees (Su et al., 2009). To this end, we first propose a smooth sigmoid surrogate (SSS) method, as an alternative to greedy search, to speed up tree construction. RFIT outperforms the traditional `separate regression' approach in estimating ITE. Furthermore, standard errors for the estimated ITE via RFIT can be obtained with the infinitesimal jackknife method. We assess and illustrate the use of RFIT via both simulation and the analysis of data from an acupuncture headache trial.

Motivation & Objective

• To address the challenge of estimating individualized treatment effects (ITE) in precision medicine using data from randomized trials.
• To reduce bias and improve accuracy in ITE estimation compared to the conventional separate regression (SR) approach.
• To develop a computationally efficient method for constructing interaction trees using a smooth sigmoid surrogate (SSS) to replace greedy search.
• To provide valid standard errors for ITE estimates via the infinitesimal jackknife method.
• To demonstrate the method’s performance through simulations and real-world data from an acupuncture headache trial.

Proposed method

• RFIT employs random forests built on interaction trees (IT) to model treatment-by-covariate interactions for ITE estimation.
• A smooth sigmoid surrogate (SSS) is introduced as a differentiable alternative to greedy search, enabling faster and more stable tree growth.
• The infinitesimal jackknife method is extended to compute standard errors for ITE estimates derived from RFIT.
• The method estimates ITE as the difference in predicted outcomes between treated and control groups within terminal nodes of the forest.
• RFIT uses bagging and ensemble averaging across multiple interaction trees to reduce variance and improve robustness.
• Covariate balance within terminal nodes is checked, and additional adjustments may be applied if imbalance is detected.

Experimental results

Research questions

• RQ1 How does RFIT compare to separate regression in estimating individualized treatment effects in terms of bias and mean squared error?
• RQ2 Can the smooth sigmoid surrogate (SSS) significantly speed up tree construction while maintaining or improving estimation accuracy?
• RQ3 Is the infinitesimal jackknife method valid for estimating standard errors of ITE estimates in the RFIT framework?
• RQ4 How well does RFIT perform in detecting heterogeneous treatment effects across different subgroups defined by covariates?
• RQ5 Does RFIT maintain good performance under varying sample sizes and data configurations?

Key findings

• RFIT significantly reduces bias in ITE estimation compared to separate regression, especially in small to moderate sample sizes (n=100 and n=500).
• With n=500, RFIT shows diminishing bias, while SR continues to exhibit substantial bias, particularly in predicting extreme ITE values.
• The range of ITE estimates from RFIT is wider than from SR, indicating lower variance and better coverage of true ITE values.
• The standard error formula derived via the infinitesimal jackknife is valid and accurately reflects the variability of ITE estimates in simulations.
• In the acupuncture headache trial, RFIT successfully identified subgroups with differential treatment effects, demonstrating practical utility.
• The SSS method accelerates tree construction and improves stability compared to greedy search, without sacrificing estimation accuracy.