# Bayesian fusion forests for heterogeneous treatment effects on survival from randomised and real-world data

arXiv: https://arxiv.org/abs/2607.29295 · HTML: https://mlsanity.com/paper/2607.29295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 23 of 23)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Survival regression with accelerated failure time model in XGBoost](https://mlsanity.com/paper/2006.04920/) (2020)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimation](https://mlsanity.com/paper/2005.10579/) (2020)
- [Individualized Treatment Effects with Censored Data via Fully Nonparametric Bayesian Accelerated Failure Time Models](https://mlsanity.com/paper/1706.06611/) (2017)
- [Data fusion methods for the heterogeneity of treatment effect and confounding function](https://mlsanity.com/paper/2007.12922/) (2020)
- [Model interpretation through lower-dimensional posterior summarization](https://mlsanity.com/paper/1905.07103/) (2019)
- [Multi-Study R-Learner for Estimating Heterogeneous Treatment Effects Across Studies Using Statistical Machine Learning](https://mlsanity.com/paper/2306.01086/) (2023)
- [A flexible parametric accelerated failure time model](https://mlsanity.com/paper/2006.06807/) (2020)
- [Incorporating External Data into the Analysis of Clinical Trials via Bayesian Additive Regression Trees](https://mlsanity.com/paper/2103.08754/) (2021)
- [Causal-ICM: A Data Fusion Framework For Heterogeneous Treatment Effect Estimation With Multi-Task Gaussian Processes](https://mlsanity.com/paper/2405.20957/) (2024)
- [Statistical Inference for Heterogeneous Treatment Effect with Right-censored Data from Synthesizing Randomized Clinical Trials and Real-world Data](https://mlsanity.com/paper/2503.15745/) (2025)
- [The causal interpretation of acceleration factors](https://mlsanity.com/paper/2409.01983/) (2024)
- [Integrative Analysis of High-dimensional RCT and RWD Subject to Censoring and Hidden Confounding](https://mlsanity.com/paper/2503.15967/) (2025)
- [Quantifying uncertainty of individualized treatment effects in right-censored survival data: A comparison of Bayesian additive regression trees and causal survival forest](https://mlsanity.com/paper/2504.04571/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Counterfactual Survival Q-learning via Buckley-James Boosting, with Applications to ACTG 175 and CALGB 8923](https://mlsanity.com/paper/2508.11060/) (2025)
- [ShrinkageTrees: An R Package for Bayesian Tree Ensembles for Survival Analysis and Causal Inference](https://mlsanity.com/paper/2606.12317/) (2026)

## Abstract (arXiv)

We develop the Bayesian fusion forest, a nonparametric framework to estimate heterogeneous treatment effects on survival outcomes by combining a randomised controlled trial and real-world data. The framework relaxes the unconfoundedness assumption on the real-world data by assuming instead that the treatment effect transports across the two sources. Our method opens up right- and interval-censored outcomes to data fusion. We model the survival time with an accelerated failure time decomposition into a shared baseline prognosis, a source-specific deviation, a treatment effect, and a confounding function. The confounding function absorbs the confounding bias in the real-world data. Each component receives a Bayesian tree ensemble prior. The shared baseline prognosis borrows strength across sources, while the deviation captures between-source heterogeneity. A hierarchical Dirichlet process mixture models the error distribution nonparametrically. A simulation study shows efficiency gains over a trial-only analysis across varying levels of confounding and between-source heterogeneity. We combine the ACTG 175 trial with the Multicenter AIDS Cohort Study to estimate the effect of combination antiretroviral therapy for HIV. The fusion identifies a benefit for nearly every patient whereas the trial alone is inconclusive.