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

TL;DR

This paper develops a method for constructing valid, shorter prediction intervals for individual treatment effects by leveraging cross-world assumptions and bounds on unidentifiable correlation, improving uncertainty quantification in causal inference.

Contribution

It introduces a novel approach using cross-world correlation bounds to refine individual treatment effect prediction intervals, enhancing stability and coverage accuracy.

Findings

Prediction intervals achieve >90% coverage in simulations.

Intervals are often less than one-third the width of existing methods.

The approach is asymptotically optimal under Gaussian assumptions.

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.