Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects

• URL: http://arxiv.org/abs/2507.12581v1
• Date: Wed, 16 Jul 2025 18:58:18 GMT
• Title: Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects
• Authors: Juraj Bodik, Yaxuan Huang, Bin Yu,
• Abstract summary: For high-stakes decision-making, individual treatment effect estimates must be accompanied by valid prediction intervals.<n>For high-stakes decision-making, individual treatment effect estimates must be accompanied by valid prediction intervals.
• Score: 6.083038976289835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While average treatment effects (ATE) and conditional average treatment effects (CATE) provide valuable population- and subgroup-level summaries, they fail to capture uncertainty at the individual level. For high-stakes decision-making, individual treatment effect (ITE) estimates must be accompanied by valid prediction intervals that reflect heterogeneity and unit-specific uncertainty. However, the fundamental unidentifiability of ITEs limits the ability to derive precise and reliable individual-level uncertainty estimates. To address this challenge, we investigate the role of a cross-world correlation parameter, $ \rho(x) = cor(Y(1), Y(0) | X = x) $, which describes the dependence between potential outcomes, given covariates, in the Neyman-Rubin super-population model with i.i.d. units. Although $ \rho $ is fundamentally unidentifiable, we argue that in most real-world applications, it is possible to impose reasonable and interpretable bounds informed by domain-expert knowledge. Given $\rho$, we design prediction intervals for ITE, achieving more stable and accurate coverage with substantially shorter widths; often less than 1/3 of those from competing methods. The resulting intervals satisfy coverage guarantees $P\big(Y(1) - Y(0) \in C_{ITE}(X)\big) \geq 1 - \alpha$ and are asymptotically optimal under Gaussian assumptions. We provide strong theoretical and empirical arguments that cross-world assumptions can make individual uncertainty quantification both practically informative and statistically valid.

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