Evaluation of "Probabilities of Causation" in Case-Control Studies: Identification and Estimation

Ryusei Shingaki, Haruka Yoshida, Manabu Kuroki
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6261-6282, 2026.

Abstract

"Probabilities of causation" play a crucial role in practical science. {Pearl} [2009] defined three types of probabilities of causation in the context of structural causal models: the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Furthermore, Tian and {Pearl} [2000] and Kuroki and Cai [2011] provided the identification conditions for these probabilities under the assumption of monotonicity. However, these identification conditions are described based on "the joint probabilities of observed probabilities" and/or "causal risks". Therefore, they are not applicable to case–control studies, in which the available statistical data are given in the form of the conditional probabilities of observed variables given an outcome variable. To address this limitation, this paper provides novel identification conditions for the probabilities of causation using (i) two proxy covariates and (ii) a proxy covariate together with an instrumental variable. Remarkably, the use of a proxy covariate and an instrumental variable enables the identification not only of the probabilities of causation but also of the joint distribution of the potential outcome variables. When these probabilities can be evaluated using the proposed identification conditions, new plug-in estimators of these probabilities are presented.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-shingaki26a, title = {Evaluation of "Probabilities of Causation" in Case-Control Studies: Identification and Estimation}, author = {Shingaki, Ryusei and Yoshida, Haruka and Kuroki, Manabu}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6261--6282}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/shingaki26a/shingaki26a.pdf}, url = {https://proceedings.mlr.press/v337/shingaki26a.html}, abstract = {"Probabilities of causation" play a crucial role in practical science. {Pearl} [2009] defined three types of probabilities of causation in the context of structural causal models: the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Furthermore, Tian and {Pearl} [2000] and Kuroki and Cai [2011] provided the identification conditions for these probabilities under the assumption of monotonicity. However, these identification conditions are described based on "the joint probabilities of observed probabilities" and/or "causal risks". Therefore, they are not applicable to case–control studies, in which the available statistical data are given in the form of the conditional probabilities of observed variables given an outcome variable. To address this limitation, this paper provides novel identification conditions for the probabilities of causation using (i) two proxy covariates and (ii) a proxy covariate together with an instrumental variable. Remarkably, the use of a proxy covariate and an instrumental variable enables the identification not only of the probabilities of causation but also of the joint distribution of the potential outcome variables. When these probabilities can be evaluated using the proposed identification conditions, new plug-in estimators of these probabilities are presented.} }
Endnote
%0 Conference Paper %T Evaluation of "Probabilities of Causation" in Case-Control Studies: Identification and Estimation %A Ryusei Shingaki %A Haruka Yoshida %A Manabu Kuroki %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-shingaki26a %I PMLR %P 6261--6282 %U https://proceedings.mlr.press/v337/shingaki26a.html %V 337 %X "Probabilities of causation" play a crucial role in practical science. {Pearl} [2009] defined three types of probabilities of causation in the context of structural causal models: the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Furthermore, Tian and {Pearl} [2000] and Kuroki and Cai [2011] provided the identification conditions for these probabilities under the assumption of monotonicity. However, these identification conditions are described based on "the joint probabilities of observed probabilities" and/or "causal risks". Therefore, they are not applicable to case–control studies, in which the available statistical data are given in the form of the conditional probabilities of observed variables given an outcome variable. To address this limitation, this paper provides novel identification conditions for the probabilities of causation using (i) two proxy covariates and (ii) a proxy covariate together with an instrumental variable. Remarkably, the use of a proxy covariate and an instrumental variable enables the identification not only of the probabilities of causation but also of the joint distribution of the potential outcome variables. When these probabilities can be evaluated using the proposed identification conditions, new plug-in estimators of these probabilities are presented.
APA
Shingaki, R., Yoshida, H. & Kuroki, M.. (2026). Evaluation of "Probabilities of Causation" in Case-Control Studies: Identification and Estimation. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6261-6282 Available from https://proceedings.mlr.press/v337/shingaki26a.html.

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