Zhehao Zhang, Thomas S. Richardson
arXiv 9 Jun 2025 · Statistics — Methodology
arXiv:2506.07469 · PDF · DOI · OpenAlex · Extracted main text
Individual treatment effect (ITE) is often regarded as the ideal target of inference in causal analyses and has been the focus of several recent studies. In this paper, we describe the intrinsic limits regarding what can be learned concerning ITEs given data from large randomized experiments. We consider when a valid prediction interval for the ITE is informative and when it can be bounded away from zero. The joint distribution over potential outcomes is only partially identified from a randomized trial. Consequently, to be valid, an ITE prediction interval must be valid for all joint distribution consistent with the observed data and hence will in general be wider than that resulting from knowledge of this joint distribution. We characterize prediction intervals in the binary treatment and outcome setting, and extend these insights to models with continuous and ordinal outcomes. We derive sharp bounds on the probability mass function (pmf) of the individual treatment effect (ITE). Finally, we contrast prediction intervals for the ITE and confidence intervals for the average treatment effect (ATE). This also leads to the consideration of Fisher versus Neyman null hypotheses. While confidence intervals for the ATE shrink with increasing sample size due to its status as a population parameter, prediction intervals for the ITE generally do not vanish, leading to scenarios where one may reject the Neyman null yet still find evidence consistent with the Fisher null, highlighting the challenges of individualized decision-making under partial identification.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lei, L. and Candès, E. J (2021) Conformal inference of counterfactuals and individual treatment effects | 0.843 | 3 | 3 | 100% |
| 2 | Fan, Y. and Park, S. S (2010) Sharp bounds on the distribution of treatment effects and their statistical inference | 0.822 | 9 | 4 | 56% |
| 3 | Zhang, Z. and Richardson, T. S (2024) Bounds on the distribution of a sum of two random variables: Revisiting a problem of kolmogorov with application to individual t… self | 0.659 | 7 | 3 | 29% |
| 4 | Frank, M. J., Nelsen, R. B., and Schweizer, B (1987) Best-possible bounds for the distribution of a sum–-a problem of kolmogorov | 0.511 | 2 | 2 | 50% |
| 5 | Lu, J., Ding, P., and Dasgupta, T (2018) Treatment effects on ordinal outcomes: Causal estimands and sharp bounds | 0.511 | 2 | 2 | 50% |
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| 7 | Dawid, A. P. and Senn, S (2023) Personalised decision-making without counterfactuals | 0.511 | 2 | 1 | 100% |
| 8 | Blaker, H (2000) Confidence curves and improved exact confidence intervals for discrete distributions | 0.405 | 1 | 1 | 100% |
| 9 | Brennan, J., Lahaie, S., Javanmard, A., Doudchenko, N., and Pouget-A… (2024) Causal bootstrap for general randomized designs | 0.405 | 1 | 1 | 100% |
| 10 | Chernozhukov, V., Wüthrich, K., and Zhu, Y (2023) Toward personalized inference on individual treatment effects | 0.405 | 1 | 1 | 100% |
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