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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]
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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
Rosenbaum, P. R. (2021) · Chapman & Hall/CRC eBooks · doi:10.1201/9781003039648-ch1 · Cited by 2
Self-citationInternal and External Validity
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Design and validation of precooked developer dashboards
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“…(1) to the best of our knowledge, we for the first time identify metrics developers want to see in dashboards, by employing an observational study [20], (2) provide a GQM model to understand why the identified metrics matter for the developers, and (3) identify how developers want to use…”
MethodThe Design of Clustered Observational Studies in Education
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“A standardized difference of less than one-tenth of a standard deviation is considered acceptable, since a randomized experiment might yield discrepancies of this size (Cochran & Rubin, 1973; Silber et al., 2001; Rosenbaum, 2010; Rosenbaum & Rubin, 1985).”
BackgroundRandomization Tests to Assess Covariate Balance When Designing and Analyzing Matched Datasets
Branson, Z. (2021) · Observational Studies · doi:10.1353/obs.2021.0031 · Cited by 22
Abar, B. W., LaGasse, L. L., Wouldes, T. A., Derauf, C., Newman, E., Shah, R., Smith, L. M., Arria, A. M., Huestis, M. A., DellaGrotta, S. A., et al. (2013) · Prevention Science · doi:10.1007/s11121-013-0431-5 · Cited by 20
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Molnar, M. Z., Potluri, V. S., Schaubel, D. E., Sise, M. E., Concepcion, B. P., Forbes, R. C., Blumberg, E. A., Bloom, R. D., Shaffer, D. R., Chung, R. T., et al. (2021) · American Journal of Transplantation · doi:10.1111/ajt.16834 · Cited by 19
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Emerging approaches to multiple chronic condition assessment
Suls, J. M., Salive, M. E., Koroukian, S. M., Alemi, F., Silber, J. H., Kastenmüller, G., & Klabunde, C. N. (2022) · Journal of the American Geriatrics Society · doi:10.1111/jgs.17914 · Cited by 19
“The algorithm identified a total of 576 QCSs; after removing redundant sets, 113 QCSs remained; 25 comorbid conditions were represented in these QCSs.”
InfluentialMammides, C., Zotos, S., & Martini, F. (2024) · Biological Conservation · doi:10.1016/j.biocon.2024.110556 · Cited by 19
Kopterides, P., Θεοδωρακοπούλου, Μ., Ilias, Ι., Nikitas, N., Frantzeskaki, F. G., Vassiliadi, D. A., Armaganidis, A., & Dimopoulou, I. (2012) · Journal of Critical Care · doi:10.1016/j.jcrc.2012.08.003 · Cited by 19
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“This work can also draw on existing empirical studies of robustness (e.g., Dong & Lipsey, 2014; Rosenbaum, 2010).”
Weld, G., West, P., Glenski, M., Arbour, D. T., Rossi, R. A., & Althoff, T. (2022) · Proceedings of the International AAAI Conference on Web and Social Media · doi:10.1609/icwsm.v16i1.19362 · Cited by 20
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“Propensity score methods attempt to replicate the distribution of background covariates that would be found in a randomized design, thereby matching covariate distributions in the treatment and comparison groups (Rosenbaum & Rubin, 1983; Rosenbaum, 2009).”
BackgroundGutman, R., & Rubin, D. B. (2015) · Statistical Methods in Medical Research · doi:10.1177/0962280215570722 · Cited by 19
Rosenbaum, P. R. (2012) · The Annals of Applied Statistics · doi:10.1214/11-aoas508 · Cited by 18
Self-citationSensitivity Analysis for the Cross-Match Test, With Applications in Genomics
Heller, R., Jensen, S. T., Rosenbaum, P. R., & Small, D. S. (2010) · Journal of the American Statistical Association · doi:10.1198/jasa.2010.ap09260 · Cited by 16
Self-citationZubizarreta, J. R., Neuman, M. D., Silber, J. H., & Rosenbaum, P. R. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.682533 · Cited by 18
Self-citationMutz, R., Wolbring, T., & Daniel, H. (2016) · Journal of the Association for Information Science and Technology · doi:10.1002/asi.23701 · Cited by 22
Discovering Heterogeneous Exposure Effects Using Randomization Inference in Air Pollution Studies
Lee, K., Small, D. S., & Dominici, F. (2021) · Journal of the American Statistical Association · doi:10.1080/01621459.2020.1870476 · Cited by 19
Kang, H., Jiang, Y., Zhao, Q., & Small, D. S. (2021) · Observational Studies · doi:10.1353/obs.2021.0029 · Cited by 18
“instrument is valid ( = 0). But, under the null hypothesis, we want to allow for the possibility that the instrument is invalid in the range 2( ;); this is referred to as the favorable situation in Rosenbaum (2010). Then, the power of being able to reject the null hypothesis in favor of this favorable alternative for…”
BackgroundMcCombs-Thornton, K. L., & Foster, E. M. (2011) · Children and Youth Services Review · doi:10.1016/j.childyouth.2011.09.013 · Cited by 18
Research Designs for Program Evaluation
Wong, V. C., Wing, C., Steiner, P. M., Wong, M., & Cook, T. D. (2012) · Wiley eBooks · doi:10.1002/9781118133880.hop202011 · Cited by 18
Why Armies Break: Explaining Mass Desertion in Conventional WarPreprint
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Health care costs of rheumatoid arthritis: A longitudinal population study
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The generalized propensity score methodology for estimating unbiased journal impact factors
Mutz, R., & Daniel, H. (2012) · Scientometrics · doi:10.1007/s11192-012-0670-4 · Cited by 17
Eeren, H. V., Goossens, L. M. A., Scholte, R. H. J., Busschbach, J. J. V., & van der Rijken, R. E. A. (2018) · Research on Child and Adolescent Psychopathology · doi:10.1007/s10802-017-0392-4 · Cited by 17
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A Semi-Parametric Approach to Model-Based Sensitivity Analysis in Observational Studies
Zhang, B., & Tchetgen, E. J. T. (2022) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12946 · Cited by 18
“…see, for example, Cornfield et al. (1959), Gastwirth et al. (1998), Scharfstein et al. (1999), McCandless et al. (2007), Ichino et al. (2008), Rosenbaum (1987b, 2002, 2010), Ding and VanderWeele (2016), Franks et al. (2020), Zhao et al. (2019) and Cinelli and Hazlett (2020), among many…”
BackgroundWho Does the Caring? Gender Disparities in COVID-19 Attitudes and Behaviors
Carreras, M., Vera, S. B., & Visconti, G. (2022) · Politics & Gender · doi:10.1017/s1743923x21000386 · Cited by 18
“Matching helps eliminate observed differences between groups to make them as comparable as possible (Rosenbaum 2010).”
BackgroundMethodInfluentialFang, H.-Y., Hsiao, F., Huang, H.-C., Lin, Y.-S., Chen, C., Shieh, S., Chen, P.-R., Chen, C.-K., & Chien, C. (2014) · Europe PMC (PubMed Central) · doi:10.3978/j.issn.2072-1439.2014.10.27 · Cited by 17
Outcome Studies of Social, Behavioral, and Educational Interventions
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Investigating Causal DIF via Propensity Score Methods.
Liu, Y., Zumbo, B., Gustafson, P., Huang, Y., Kroc, E., & Wu, A. (2016) · Scholarworks (University of Massachusetts Amherst) · doi:10.7275/ewqz-n963 · Cited by 19
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“data est_sbcY1&j; set est_sbcY1&j; if class="Diff (1-2)" then MeanrevY1=-1*Mean; run;”
BackgroundInfluentialCausal Inference Strategies in Corporate Governance ResearchPreprint
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The Trouble with Instruments: The Need for Pre-Treatment Balance in Shock-IV DesignsPreprint
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Using statistical methods to model the fine-tuning of molecular machines and systems
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“It is well known that sometimes (but not always) the likelihood of such a study needs to be adjusted in order to account for the way in which the past event was observed, also within a Bayesian approach (Rosenbaum, 2010).”
BackgroundAmbiguous Dynamic Treatment Regimes: A Reinforcement Learning Approach
Saghafian, S. (2023) · Management Science · doi:10.1287/mnsc.2022.00883 · Cited by 23
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The Impact Of Decision Aids On Adults Considering Hip Or Knee Surgery
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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).”
BackgroundZhang, X., & Wu, Y. (2022) · Frontiers in Environmental Science · doi:10.3389/fenvs.2022.946993 · Cited by 16
“Thus, the quasi-natural experiment of hosting comprehensive sports events violated the SUTVA, and using the traditional DID model to assess the impact of hosting comprehensive sports events on the green and low-carbon development will lead to biased estimation results (Delgado and Florax, 2015).”
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“Fortunately, the potential outcomes framework advanced by Neyman (1935) and Rubin (1973, 1974) as well as Rosenbaum (2010) provide a roadmap for conducting causal inference using observational data.”
BackgroundWallace, G. P. R. (2019) · Law & Social Inquiry · doi:10.1017/lsi.2018.22 · Cited by 16
“…from those reported earlier based on more conventional OLS regression models.35 Of course, the reliability of any matching findings depends on the assumption that assignment to the treatment group (knowledge of the Geneva Conventions) is captured by the observed covariates (Rosenbaum 2010, 76–79).”
BackgroundSmall, D. S., Sorenson, S. B., & Berk, R. A. (2019) · Journal of Behavioral Medicine · doi:10.1007/s10865-019-00013-8 · Cited by 15
A Negative Correlation Strategy for Bracketing in Difference-in-Differences
Ye, T., Keele, L. J., Hasegawa, R. B., & Small, D. S. (2023) · Journal of the American Statistical Association · doi:10.1080/01621459.2023.2252576 · Cited by 15
“To enhance the reliability of an observational study, it is useful to include additional analyses that explore whether the key assumptions appear plausible and whether conclusions are robust to violations of the key assumptions (Rosenbaum 2010).”
Risk-based loan pricing consequences for credit unions
Walke, A. G., Fullerton, T. M. J., & Tokle, R. J. (2018) · Journal of Empirical Finance · doi:10.1016/j.jempfin.2018.02.006 · Cited by 15
Living with observational data in biological anthropology
Smith, R. J. (2019) · American Journal of Physical Anthropology · doi:10.1002/ajpa.23862 · Cited by 16
Nattino, G., Lü, B., Shi, J., Lemeshow, S. A., & Xiang, H. (2020) · Journal of the American Statistical Association · doi:10.1080/01621459.2020.1737078 · Cited by 15
“Using matched design in causal inference is well established for studies with two treatment arms (Hansen 2004; Rosenbaum 2010a; Austin 2014).”
BackgroundMethodInfluentialMudombi, S., Ochieng, C., Johnson, F. X., von Maltitz, G. P., Luhanga, D., Dompreh, E. B., Romeu–Dalmau, C., & Gasparatos, A. (2021) · Energy Research & Social Science · doi:10.1016/j.erss.2021.102053 · Cited by 17
“Matching quality Covariate balance checks can indicate whether the treated and control groups have the sufficient overlap needed for matching and if the balance derived from the matching is reasonable [82].”
BackgroundGoodman‐Scott, E., McMahon, G., Kalkbrenner, M. T., Smith-Durkin, S., Patel, S. I., Czack, A., & Weeks, N. (2021) · Journal of Positive Behavior Interventions · doi:10.1177/10983007211013784 · Cited by 19
“Based on the recommendations of Rosenbaum (2010), we aimed for an approximately 1:3 sampling ratio of PBIS schools to comparison (nonPBIS) schools to reduce the error of the estimated difference between the PBIS schools and comparison schools.”
MethodFaries, D. E., Chen, Y., Lipkovich, I. A., Zagar, A. J., Liu, X., & Obenchain, R. L. (2013) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.1390 · Cited by 15
Earnout financing in the financial services industry
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Dexrazoxane preferentially mitigates doxorubicin cardiotoxicity in female children with sarcoma
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“We created a propensity score for the receipt of dexrazoxane using the subcohort of subjects who were treated before dexrazoxane use was universal.(19) We used logistic regression to determine a propensity for the receipt of dexrazoxane, and applied this propensity to the overall cohort.”
MethodMortality Rate Estimation and Standardization for Public Reporting: Medicare’s Hospital Compare
George, E. I., Ročková, V., Rosenbaum, P. R., Satopää, V., & Silber, J. H. (2017) · ScholarlyCommons (University of Pennsylvania) · doi:10.6084/m9.figshare.4572694.v2 · Cited by 15
Self-citationNew Perspectives on Causal Mediation Analysis
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Improving the design stage of air pollution studies based on wind patterns
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Conventional versus organic olive farming: which has a better economic performance?
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“(4) In randomized experiments, the abovementioned condition is automatically assumed since the assignment of subjects to the treatment group is completely random (Rosenbaum 2010; Stuart 2010).”
BackgroundAssessing lung cancer progression and survival with infrared spectroscopy of blood serum
Kepesidis, K. V., Stoleriu, M.-G., Feiler, N., Gigou, L., Fleischmann, F., Aschauer, J., Eiselen, S., Koch, I., Reinmuth, N., Tufman, A., et al. (2025) · BMC Medicine · doi:10.1186/s12916-025-03924-3 · Cited by 14
African American Turnout in Majority-Minority Districts
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Influence of key role players on productivity outcomes in the residential building lifecycle
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The probability of a robust inference for internal validity
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“…can make causal inference between two variables given they are correlated, is frequently challenged and difficult to assess for observational studies (Imai, King, and Stuart 2008; Imbens and Rubin 2015; Murnane and Willett 2011; Rosenbaum 2002, 2010; Rosenbaum and Rubin 1983a; Shadish et al. 2002).”
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Rebar: Reinforcing a Matching Estimator With Predictions From High-Dimensional Covariates
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Optimally Balanced Gaussian Process Propensity Scores for Estimating Treatment Effects
Vegetabile, B., Gillen, D. L., & Stern, H. S. (2019) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12502 · Cited by 14
“Although this is a clear limitation of observational studies, there have been many proposed methods to address the sensitivity of estimates of treatment effects to the presence of potentially unobserved confounding variables (e.g. the methods that were outlined in Rosenbaum (2010)).”
MethodCerna-Turoff, I., Kane, J. C., Devries, K. M., Mercy, J. A., Massetti, G. M., & Baiocchi, M. (2020) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2020.104393 · Cited by 14
LURKING INFERENTIAL MONSTERS? QUANTIFYING SELECTION BIAS IN EVALUATIONS OF SCHOOL PROGRAMS
Weidmann, B., & Miratrix, L. W. (2020) · Journal of Policy Analysis and Management · doi:10.1002/pam.22236 · Cited by 13
Weighted nearest neighbours-based control group selection method for observational studies
Szekér, S., & Vathy-Fogarassy, Á. (2020) · PLoS ONE · doi:10.1371/journal.pone.0236531 · Cited by 15
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INTERPOL's Surveillance Network in Curbing Transnational Terrorism
Gardeazábal, J., & Sandler, T. M. (2015) · Journal of Policy Analysis and Management · doi:10.1002/pam.21845 · Cited by 14
Customer price sensitivities in competitive insurance markets
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“Following Rosenbaum (2010), we used a caliper distance of 0.2 of the standard deviation of the estimated propensity scores.”
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Accounting for Nonignorable Unit Nonresponse and Attrition in Panel Studies with Refreshment Samples
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Evaluating and improving a matched comparison of antidepressants and bone density
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“Common strategies for balancing an identified feature include near-fine balance (Yang et al., 2012), near-exact match (Rosenbaum, 2010, § 9.2), nondirectional, and directional penalties (Yu and Rosenbaum, 2019).”
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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
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