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Recursive partitioning for heterogeneous causal effects
Open accessAbstract
In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without “sparsity” assumptions. We propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7–22%.
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“In particular, Athey and Imbens (2016), Wager and Athey (2018), and Athey et al. (2019) developed random forests methods designed to capture honest heterogeneity in treatment effects, circumventing overfitting issues inherent to traditional methods and thus avoiding mistaking statistical noise for heterogeneity.”
From Prison Rehabilitation Programs: Efficiency and Targeting (2021) · cites this paper as Athey and Imbens (2016)
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Metadata
- Authors
- Athey, S., & Imbens, G.
- Affiliations
- Stanford University (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2016-07-05
- Volume
- 113
- Issue
- 27
- Pages
- 7353-7360
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC4941430
- OpenAlex
- W2305754340
- Cited by
- 1,586
- References
- 43
- Citations by year
- 2026: 213 · 2025: 235 · 2024: 198 · 2023: 175 · 2022: 170 · 2021: 178 · 2020: 161 · 2019: 110 · 2018: 66 · 2017: 61 · 2016: 15
- FWCI
- 87.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Deep Blue (University of Michigan) (submittedVersion)
- Funders
- Microsoft Research (0)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- treatment effect heterogeneity, recursive partitioning, regression trees, cross-validation, model selection criteria, high-dimensional covariates, causal inference
- MeSH terms
- Machine Learning, Computer Simulation, Models, Theoretical, Research Design, Statistics as Topic
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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