Probabilities of Causation for Continuous Outcomes: Bounds and Identification
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913084605464576 |
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| author | Chaoge, Jile Han, Kesen Liu, Fahui Wu, Peng |
| author_facet | Chaoge, Jile Han, Kesen Liu, Fahui Wu, Peng |
| contents | The probability of necessity (PN), which quantifies the probability that an observed event would not have occurred in the absence of the treatment, is a central estimand in attribution analysis. While PN has been extensively studied for binary outcomes and has recently been developed for ordinal outcomes, a formal framework for continuous outcomes remains underdeveloped. To address this gap, we propose the general probability of necessity (GPN) for continuous outcomes, a setting that is substantially more challenging than the binary and ordinal cases. Rather than imposing strong identifiability assumptions, we adopt a partial identification perspective and derive sharp lower and upper bounds under standard assumptions of ignorability and monotonicity. We further introduce a copula-based framework that exploits dependence information between potential outcomes to tighten these bounds. Simulation studies and real-world applications demonstrate the effectiveness of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01883 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probabilities of Causation for Continuous Outcomes: Bounds and Identification Chaoge, Jile Han, Kesen Liu, Fahui Wu, Peng Methodology The probability of necessity (PN), which quantifies the probability that an observed event would not have occurred in the absence of the treatment, is a central estimand in attribution analysis. While PN has been extensively studied for binary outcomes and has recently been developed for ordinal outcomes, a formal framework for continuous outcomes remains underdeveloped. To address this gap, we propose the general probability of necessity (GPN) for continuous outcomes, a setting that is substantially more challenging than the binary and ordinal cases. Rather than imposing strong identifiability assumptions, we adopt a partial identification perspective and derive sharp lower and upper bounds under standard assumptions of ignorability and monotonicity. We further introduce a copula-based framework that exploits dependence information between potential outcomes to tighten these bounds. Simulation studies and real-world applications demonstrate the effectiveness of our method. |
| title | Probabilities of Causation for Continuous Outcomes: Bounds and Identification |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.01883 |