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March 2024 A Bayesian machine learning approach for estimating heterogeneous survivor causal effects: Applications to a critical care trial
Xinyuan Chen, Michael O. Harhay, Guangyu Tong, Fan Li
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Ann. Appl. Stat. 18(1): 350-374 (March 2024). DOI: 10.1214/23-AOAS1792


Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development in tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for many participants in which case principal stratification is an appealing framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate mean models for the potential outcomes and latent stratum membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by biologic sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and degree of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field.

Funding Statement

Research in this article was partially supported by the Patient-Centered Outcomes Research Institute® (PCORI® Awards ME-2020C1-19220 to M.O.H. and ME-2020C3-21072 to F.L).
M.O.H. is funded by the United States National Institutes of Health (NIH), National Heart, Lung, and Blood Institute (NHLBI, grant number R00-HL141678).
X.C., F.L., and M.O.H. are funded by the NIH/NHLBI (grant number R01-HL168202).
All statements in this report, including its findings and conclusions, are solely those of the authors and do not necessarily represent the views of the NIH or PCORI® or its Board of Governors or Methodology Committee.


The authors would like to extend their gratitude, without any implication for any errors in reporting or interpretation, to Drs. Douglas Hayden, B. Taylor Thompson, Scott Halpern, and Nadir Yehya for assistance with various questions during the development of this manuscript.


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Xinyuan Chen. Michael O. Harhay. Guangyu Tong. Fan Li. "A Bayesian machine learning approach for estimating heterogeneous survivor causal effects: Applications to a critical care trial." Ann. Appl. Stat. 18 (1) 350 - 374, March 2024.


Received: 1 April 2022; Revised: 1 June 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1792

Keywords: Acute lung injury , Bayesian additive regression trees , Causal inference , heterogeneity of treatment effects , Principal stratification , truncation by death

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.18 • No. 1 • March 2024
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