A hierarchical modelling approach for Bayesian Causal Forests on longitudinal data: A Case Study in Multiple Sclerosis Clinical Trials

TL;DR

This paper introduces BCFLong, a hierarchical Bayesian model extending Bayesian Causal Forests to handle longitudinal data, effectively capturing within-individual correlations and improving causal inference in clinical trials like MS.

Contribution

The paper develops BCFLong, a novel hierarchical Bayesian model that enhances causal inference in longitudinal studies by modeling within-individual correlations and heterogeneity.

Findings

BCFLong outperforms existing models in simulations.

It captures meaningful longitudinal patterns in MS brain volume data.

Demonstrates robustness to data sparsity.

Abstract

Long-running clinical trials offer a unique opportunity to study disease progression and treatment response over time, enabling questions about how and when interventions alter patient trajectories. However, drawing causal conclusions in this setting is challenging due to irregular follow-up, individual-level heterogeneity, and time-varying confounding. Bayesian Additive Regression Trees (BART) and their extension, Bayesian Causal Forests (BCF), have proven powerful for flexible causal inference in observational data, especially for heterogeneous treatment effects and non-linear outcome surfaces. Yet, both models assume independence across observations and are fundamentally limited in their ability to model within-individual correlation over time. This limits their use in real-world longitudinal settings where repeated measures are the norm. Motivated by the NO.MS dataset, the largest and most comprehensive clinical trial dataset in Multiple Sclerosis (MS), with more than 35,000 patients and up to 15 years follow-up, we develop BCFLong, a hierarchical model that preserves BART's strengths while extending it for longitudinal analysis. Inspired by BCF, we decompose the mean into prognostic and treatment effects, modelling the former on Image Quality Metrics (IQMs) to account for scanner effects, and introduce individual-specific random effects, including intercepts and slope, with a sparsity-inducing horseshoe prior. Simulations confirm BCFLong's superior performance and robustness to sparsity, significantly improving outcome and treatment effect estimation. On NO.MS, BCFLong captures clinically meaningful longitudinal patterns in brain volume change, which would have otherwise remained undetected. These findings highlight the importance of adaptively accounting for within-individual correlations and position BCFLong as a flexible framework for causal inference in longitudinal data.