Bayesian Causal Forests for Zero-Inflated Continuous Outcomes
Abstract
Estimating (heterogeneous) treatment effects is still challenging when the outcome is semicontinuous (i.e., exhibiting both a discrete point mass at zero and a skewed continuous distribution for positive values), despite the strong presence of this data type in real world settings. Existing methods either ignore the zero mass, impose fragile parametric assumptions, or suffer from extreme computational costs and data augmentation noise. This paper proposes Zero-Inflated Continuous Bayesian Causal Forests with Duan's Smearing (ZIC-BCF-Smear), a decoupled two-part nonparametric estimator that fits a Probit BCF on the full sample to model participation and a Gaussian BCF strictly on the active subpopulation to model positive intensity. Subpopulation Propensity Adjustment (SPA) mitigates regularization-induced confounding within the active subpopulation, and Duan's non-parametric smearing estimator re-transforms predictions to the response scale, bypassing the fragile scale multipliers of parametric models. A comprehensive simulation benchmark shows that ZIC-BCF-Smear matches well-specified parametric models without their assumptions and remains stable and calibrated where competitors either diverge or pathologically over-cover for nonlinear data. The method is then applied to individual-participant data from the SPECTRUM randomized phase III head-and-neck cancer trial, estimating the causal effect of assignment to panitumumab plus chemotherapy on the number of days patients spend with severe toxicity, an outcome for which a quarter of patients contribute an exact zero. Panitumumab assignment raises that burden by about ten days per patient under the trial's own differential treatment duration, and the decoupled structure localizes the effect mainly in the positive-intensity part rather than in whether the reconstructed severe-AE burden is positive.
Related
- Factorial Multivariate Bayesian Causal Forests: heterogeneous main and interaction effects of multiple treatments on correlated outcomes
- Dirichlet-Tree Allocation Priors for Bayesian Causal Forests
- Wasserstein Causal Forests for Distribution-Valued Outcomes
- Credible Bounds for Causal Quantities with Continuous Outcomes
- Is the treatment beneficial? Causal Inference with Ordinal Outcomes: A Bayesian Solution
BibTeX
@misc{souto2026bayesian,
title = {{Bayesian Causal Forests for Zero-Inflated Continuous Outcomes}},
author = {Hugo Gobato Souto and Eric Wang and Igor Shuryak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18889},
eprint = {2610.18889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18889},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian Causal Forests for Zero-Inflated Continuous Outcomes
AU - Hugo Gobato Souto
AU - Eric Wang
AU - Igor Shuryak
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.18889
UR - https://arxiv.org/abs/2610.18889
AB - Estimating (heterogeneous) treatment effects is still challenging when the outcome is semicontinuous (i.e., exhibiting both a discrete point mass at zero and a skewed continuous distribution for positive values), despite the strong presence of this data type in real world settings. Existing methods either ignore the zero mass, impose fragile parametric assumptions, or suffer from extreme computational costs and data augmentation noise. This paper proposes Zero-Inflated Continuous Bayesian Causal Forests with Duan's Smearing (ZIC-BCF-Smear), a decoupled two-part nonparametric estimator that fits a Probit BCF on the full sample to model participation and a Gaussian BCF strictly on the active subpopulation to model positive intensity. Subpopulation Propensity Adjustment (SPA) mitigates regularization-induced confounding within the active subpopulation, and Duan's non-parametric smearing estimator re-transforms predictions to the response scale, bypassing the fragile scale multipliers of parametric models. A comprehensive simulation benchmark shows that ZIC-BCF-Smear matches well-specified parametric models without their assumptions and remains stable and calibrated where competitors either diverge or pathologically over-cover for nonlinear data. The method is then applied to individual-participant data from the SPECTRUM randomized phase III head-and-neck cancer trial, estimating the causal effect of assignment to panitumumab plus chemotherapy on the number of days patients spend with severe toxicity, an outcome for which a quarter of patients contribute an exact zero. Panitumumab assignment raises that burden by about ten days per patient under the trial's own differential treatment duration, and the decoupled structure localizes the effect mainly in the positive-intensity part rather than in whether the reconstructed severe-AE burden is positive.
ER -