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

arXiv:2507.12581v2 Announce Type: replace-cross
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 $Pbig(Y(1) – Y(0) in C_{ITE}(X)big) geq 1 – alpha$ 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.