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“Interestingly, this score has a balancing property that states that if customers have the same propensity score, then the difference in their risk characteristics is independent of the assigned treatment, or 𝑇 𝑖 ⟂ 𝑿 𝑖 |𝜋(𝑡 𝑐 , 𝑿 𝑖 ) ∀𝑐 ∈ {1, … , 𝐶} (Guo & Fraser, 2009;Imbens, 2004;Rosenbaum, 2010).”
From Customer price sensitivities in competitive insurance markets (2022) · cites this paper as Rosenbaum, 2010
In the citing paper
“We recognize, of course, that quasi-experimental methods such as instrumental variables and regression discontinuity designs allow for causal conclusions to be drawn from observational snapshots when investigators make strong, explicit assumptions and articulate a credible identification strategy 27-30 .”
From Quantifying the prevalence and impact of overreaching causal claims in social science (2026) · cites this paper as [27]
Citations
Cites
The Bias Due to Incomplete Matching
Rosenbaum, P. R., & Rubin, D. B. (1985) · Biometrics · doi:10.2307/2530647 · Cited by 532
Self-citationDoes Cardiac Transplantation Prolong Life?
Gail, M. H. (1972) · Annals of Internal Medicine · doi:10.7326/0003-4819-76-5-815 · Cited by 124
Causal Inference in Randomized Experiments
Rosenbaum, P. R. (2009) · Springer series in statistics · doi:10.1007/978-1-4419-1213-8_2 · Cited by 10
Self-citationCompeting Theories Structure Design
Rosenbaum, P. R. (2009) · Springer series in statistics · doi:10.1007/978-1-4419-1213-8_4 · Cited by 4
Self-citationTwo Simple Models for Observational Studies
Rosenbaum, P. R. (2009) · Springer series in statistics · doi:10.1007/978-1-4419-1213-8_3 · Cited by 3
Self-citationUncommon but Dramatic Responses to Treatment
Rosenbaum, P. R. (2009) · Springer series in statistics · doi:10.1007/978-1-4419-1213-8_16 · Cited by 2
Self-citationRosenbaum, P. R. (1995) · Springer series in statistics · doi:10.1007/978-1-4757-2443-1_7 · Cited by 2
Self-citationCausal Inference in Randomized Experiments
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Self-citationInternal and External Validity
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“This threshold is known as the design sensitivity and depends not only on the alternative but on the test statistic (Rosenbaum, 2010 a , § 14).”
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“Finally, to ensure suf fi cient and reproducible research studies, we strongly encourage the use of reporting guidelines to improve the accuracy and transparency of reporting observational studies (55, 56).”
BackgroundMethodBalancing Weights for Estimating Treatment Effects in Educational Studies
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“We provide a brief review of sensitivity analyses, but readers should see Rosenbaum (2010) for more details and Page et al. (2020) for a detailed example in the education research context.”
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“Both MAPD and Algorithm 1 use the same cost function, which is the rank based robust Mahalanobis distance of the two covariates (Rosenbaum, 2010, section 8.3).”
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“To overcome this problem, we employ propensity score matching developed by Rosenbaum and Rubin (1983) (see Rosenbaum 2010; Imbens and Rubin 2015; Morgan and Winship 2015 for surveys).”
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“However, in the case of testing the null hypothesis of no average treatment effect, simulation studies showed that a FRT that uses rank data has good error rates across different simulation conditions (Imbens & Rubin, 2015; Rosenbaum, 2002, 2010).”
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“The bounds in Proposition 2 are exact, and their exact values can be easily obtained by convolving probability generating functions (Rosenbaum 2010, chap.”
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“Due to its capacity for dealing with outliers and rare categories (Rosenbaum, 2010), the selected method was the nearest neighbor matching using the robust rank-based Mahalanobis distance.”
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“There is past work on validating assumptions of causal models to the extent possible, often by exploring the sensitivity of the obtained estimate to unobserved variables [8, 24, 25].”
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“For more comprehensive discussion of observational studies, see Altmann (1974), McKinlay (1975), and Rosenbaum, Rosenbaum, and Briskman (2010), among others.”
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“One approach omitted from thisdiscussion,whichmany investigators finduseful, is permutation-based inference (Rosenbaum 2002, 2010).”
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“In a matched observational study, subjects with comparable measured confounders are put into matched sets and inferences are drawn based on comparisons within these matched sets (Rosenbaum, 2002, 2010a; Hansen, 2004; Stuart, 2010; Lu et al., 2011; Zubizarreta, 2012; Pimentel et al., 2015).”
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“Additionally, we employed the Rosenbaum bounds method to assess the sensitivity of the average treatment effect on the treated estimates to unobservable variables (Rosenbaum, 2010).”
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“Testing itself is complementary to other objectives, including optimization of observed balance to estimate treatment effects as well as sensitivity analysis (Rosenbaum 2010).”
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“To assess covariate balance, formal tests can also be used, namely the Wilcoxon rank sum test for continuous variables and Fisher’s exact test for binary variables (Rosenbaum 2010, p. 189).”
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Metadata
- Authors
- Rosenbaum, P. R.
- Affiliations
- University of Pennsylvania (US)
- Corresponding author
- Rosenbaum, Paul R.
- ORCID
- Rosenbaum, Paul R.
- Venue
- Springer Series in Statistics
- Publisher
- Springer New York
- Published
- 2010
- ISSN
- 0172-7397 (ISSN-L)
- OpenAlex
- W253646976
- Cited by
- 1,150
- References
- 12
- Citations by year
- 2026: 33 · 2025: 72 · 2024: 58 · 2023: 58 · 2022: 73 · 2021: 115 · 2020: 108 · 2019: 71 · 2018: 73 · 2017: 68 · 2016: 75 · 2015: 85 · 2014: 84 · 2013: 58 · 2012: 55
- FWCI
- 6.61
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- Locations
- Springer series in statistics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- observational studies, research design, causal inference, statistical inference, confounding
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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