# On Heterogeneous Treatment Effects in Heterogeneous Causal Graphs

arXiv: https://arxiv.org/abs/2301.12383 · HTML: https://mlsanity.com/paper/2301.12383/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 29 Jan 2023.

## Builds on (most cited first, 15 of 15)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical Models](https://mlsanity.com/paper/1809.10652/) (2018)
- [Testing Mediation Effects Using Logic of Boolean Matrices](https://mlsanity.com/paper/2005.04584/) (2020)

## Built on by (most cited first, 2 of 2)

- [Transparency challenges in policy evaluation with causal machine learning -- improving usability and accountability](https://mlsanity.com/paper/2310.13240/) (2023)
- [Diagnosing and Rectifying Fake OOD Invariance: A Restructured Causal Approach](https://mlsanity.com/paper/2312.09758/) (2023)

## Abstract (arXiv)

Heterogeneity and comorbidity are two interwoven challenges associated with various healthcare problems that greatly hampered research on developing effective treatment and understanding of the underlying neurobiological mechanism. Very few studies have been conducted to investigate heterogeneous causal effects (HCEs) in graphical contexts due to the lack of statistical methods. To characterize this heterogeneity, we first conceptualize heterogeneous causal graphs (HCGs) by generalizing the causal graphical model with confounder-based interactions and multiple mediators. Such confounders with an interaction with the treatment are known as moderators. This allows us to flexibly produce HCGs given different moderators and explicitly characterize HCEs from the treatment or potential mediators on the outcome. We establish the theoretical forms of HCEs and derive their properties at the individual level in both linear and nonlinear models. An interactive structural learning is developed to estimate the complex HCGs and HCEs with confidence intervals provided. Our method is empirically justified by extensive simulations and its practical usefulness is illustrated by exploring causality among psychiatric disorders for trauma survivors.