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arXiv · 2605.01883

Probabilities of Causation for Continuous Outcomes: Bounds and Identification

Jile Chaoge·Kesen Han·Fahui Liu·Peng Wu
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Abstract

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.

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Jile Chaoge, Kesen Han, Fahui Liu, Peng Wu. 2026-05-03. Probabilities of Causation for Continuous Outcomes: Bounds and Identification. https://arxiv.org/abs/2605.01883

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