Causal Attribution Analysis for Continuous Outcomes

Shanshan Luo, Yu Yixuan, Chunchen Liu, Feng Xie, Zhi Geng
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:41468-41493, 2025.

Abstract

Previous studies have extensively addressed the attribution problem for binary outcome variables. However, in many practical scenarios, the outcome variable is continuous, and simply binarizing it may result in information loss or biased conclusions. To address this issue, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous outcome. These estimands include posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-luo25q, title = {Causal Attribution Analysis for Continuous Outcomes}, author = {Luo, Shanshan and Yixuan, Yu and Liu, Chunchen and Xie, Feng and Geng, Zhi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {41468--41493}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/luo25q/luo25q.pdf}, url = {https://proceedings.mlr.press/v267/luo25q.html}, abstract = {Previous studies have extensively addressed the attribution problem for binary outcome variables. However, in many practical scenarios, the outcome variable is continuous, and simply binarizing it may result in information loss or biased conclusions. To address this issue, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous outcome. These estimands include posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.} }
Endnote
%0 Conference Paper %T Causal Attribution Analysis for Continuous Outcomes %A Shanshan Luo %A Yu Yixuan %A Chunchen Liu %A Feng Xie %A Zhi Geng %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-luo25q %I PMLR %P 41468--41493 %U https://proceedings.mlr.press/v267/luo25q.html %V 267 %X Previous studies have extensively addressed the attribution problem for binary outcome variables. However, in many practical scenarios, the outcome variable is continuous, and simply binarizing it may result in information loss or biased conclusions. To address this issue, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous outcome. These estimands include posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.
APA
Luo, S., Yixuan, Y., Liu, C., Xie, F. & Geng, Z.. (2025). Causal Attribution Analysis for Continuous Outcomes. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:41468-41493 Available from https://proceedings.mlr.press/v267/luo25q.html.

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