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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
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Self-citationCausal Inference in Randomized Experiments
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Self-citationInternal and External Validity
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Items 701–800 of 1,002
Gao, Z., Guo, Z., & Tang, Q. (2021) · Information Systems and e-Business Management · doi:10.1007/s10257-021-00515-6 · Cited by 5
“As a general rule, the standardized mean deviation (SMD) of variables between matched and unmatched loans should be no larger than 0.2 (or preferably 0.1) if the two loan groups are well balanced (Rosenbaum 2010).”
BackgroundInfluentialHeng, S., O’Meara, W. P., Simmons, R., & Small, D. S. (2021) · eLife · doi:10.7554/elife.65133 · Cited by 6
“…approach (Card and Krueger, 2000; Abadie, 2005; Athey and Imbens, 2006; Angrist and Pischke, 2008; Dimick and Ryan, 2014; St.Clair and Cook, 2015) combined with matching (Rubin, 1973, 2006; Rosenbaum, 2002, 2010; Hansen, 2004; Stuart, 2010; Zubizarreta, 2012; Pimentel et al., 2015).”
BackgroundMethodInfluentialA Quasi-Experimental Study on the Effects of Community versus Custodial Sanctions in Youth Justice
Koops-Geuze, G. J., Wermink, H. T., & Weerman, F. M. (2022) · Youth Violence and Juvenile Justice · doi:10.1177/15412040221133094 · Cited by 5
“Thus, the propensity score for each case/youth is a total value that is calculated based on the combined scores of each covariate included in the model (Rosenbaum, 2010).”
BackgroundInfluentialKarnick, C., Modany, A., McGraw, M., Ludwig, J. M., Marr, D., Hammonds, T. L., Good, C. B., & Culley, E. J. (2022) · Journal of Managed Care & Specialty Pharmacy · doi:10.18553/jmcp.2022.28.11.1304 · Cited by 7
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Truth or Truthiness: Distinguishing Fact from Fiction by Learning to Think Like a Data Scientist
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Zur Verhaltensvalidität von Vignettenexperimenten
Petzold, K., & Wolbring, T. (2018) · Schriftenreihe der ASI - Arbeitsgemeinschaft Sozialwissenschaftlicher Institute · doi:10.1007/978-3-658-24517-7_10 · Cited by 2
The scarring effects of youth joblessness in Sri Lanka
Kuchibhotla, M., Orazem, P. F., & Ravi, S. (2019) · Review of Development Economics · doi:10.1111/rode.12639 · Cited by 5
“4 Evidence is presented in Rosenbaum (2010), who defines an observational study as “an empiric investigation of treatment effects when random assignment to treatment or control is not feasible.””
Bachmann, S., Haffer, S., Beschoner, P., & Viviani, R. (2011) · Schizophrenia Research · doi:10.1016/j.schres.2011.07.023 · Cited by 5
Estimation under model uncertainty
Longford, N. T. (2017) · Statistica Sinica · doi:10.5705/ss.202015.0212 · Cited by 5
Gelman, A., & O’Rourke, K. (2014) · Springer eBooks · doi:10.1007/978-3-319-05467-4_10 · Cited by 5
Nonreactive and Purely Reactive Doses in Observational Studies
Rosenbaum, P. R. (2012) · Wiley series in probability and statistics · doi:10.1002/9781119945710.ch19 · Cited by 5
Self-citationFresh Fruit and Vegetable Consumption: The Impact of Access and ValuePreprint
Levi, R., Paulson, E., & Perakis, G. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3691925 · Cited by 5
Bo, H., & Galiani, S. (2019) · National Bureau of Economic Research · doi:10.3386/w26422 · Cited by 5
“Though this distance is the most commonly used measure in the literature, there are many alternative matching criteria (Rosenbaum, 2010) that researchers can use for their specific purposes.”
Congress, Public Opinion, and Representation in the One-Party South, 1930s-1960s
Caughey, D. (2012) · eScholarship (California Digital Library) · Cited by 5
Dominici, F., Bargagli-Stoffi, F. J., & Mealli, F. (2021) · Harvard Data Science Review · doi:10.1162/99608f92.8102afed · Cited by 19
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“Parallel to what a power test does for an experiment, the sensitivity analysis in matching algorithms aims to distinguish treatment effects from bias due to unmeasured covariates (Rosenbaum, 2010).”
Review: propensity score methods with application to the HELP clinic clinical study
Rai, S. N., Wu, X., Srivastava, D. K., Craycroft, J. A., Rai, J. P., Srivastava, S., James, R. F., Boakye, M., Bhatnagar, A., & Baumgartner, R. (2018) · Open Access Medical Statistics · doi:10.2147/oams.s156704 · Cited by 4
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“We adopted the missing indicator approach [42] for variables that contained missing values and used a censoring approach to alleviate the influence of extreme outliers common in health care data.”
MethodSchochet, P. Z. (2022) · Journal of Causal Inference · doi:10.1515/jci-2022-0033 · Cited by 3
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“[15].”
Juvenile sanctions for young adult offenders in the Netherlands: an opportunity for rehabilitation?
Prop, L. J. C., van der Laan, A. M., Beerthuizen, M. G. C. J., Barendregt, C. S., & van Nieuwenhuizen, C. (2025) · Child and Adolescent Psychiatry and Mental Health · doi:10.1186/s13034-025-00888-3 · Cited by 4
“Propensity score matching is a statistical technique used to reduce selection bias in observational studies [32, 33].”
Design sensitivity and its implications for weighted observational studies
Huang, M., Soriano, D., & Pimentel, S. D. (2025) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1093/jrsssa/qnaf067 · Cited by 4
“Design sensitivity in this formal sense was introduced by Rosenbaum (2004) and has been explored extensively for matched studies (Heller et al., 2009; Rosenbaum, 2010b; Hsu et al., 2013).”
Jin, Y., Kostadinov, D. D., Bouzid, M., & Aghasaryan, A. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-19945-6_8 · Cited by 4
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Social distancing and COVID-19: Randomization inference for a structured dose-response relationship
Zhang, B., Heng, S., Ye, T., & Small, D. S. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1613 · Cited by 4
“…distribution entering statistical inference is the randomization distribution that describes the treatment dose assignment; therefore, the key step here is to properly embed the observational data into an approximately randomized experiment via statistical matching (Rosenbaum, 2002, 2010).”
BackgroundMethodInfluentialExploiting Equality Constraints in Causal Inference
Zhang, C., Cinelli, C., Chen, B., & Pearl, J. (2021) · International Conference on Artificial Intelligence and Statistics · Cited by 4
Constructing generalizable geographic natural experiments
Kuffuor, O., Visconti, G., & Young, K. (2022) · Research & Politics · doi:10.1177/20531680221113763 · Cited by 4
“…to explore some of the most elusive questions about the political world, characterized by circumstances that allow researchers to assume as-if random or haphazard treatment conditions even though treatment allocation is not defined by a random device (Rosenbaum, 2010; Dunning, 2012; Keele, 2015).”
BackgroundPetzold, K., & Netz, N. (2022) · Higher education research and science studies · doi:10.1007/978-3-658-36921-7_7 · Cited by 4
How Well Can Fine Balance Work for Covariate Balancing
Yu, R. (2022) · Biometrics · doi:10.1111/biom.13771 · Cited by 4
O, A. L. D. L., Fernández-Vázquez, P., & García, F. M. (2023) · Journal of Development Economics · doi:10.1016/j.jdeveco.2022.103043 · Cited by 4
Yu, R., Kelz, R. R., Lorch, S. A., & Keele, L. J. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1691 · Cited by 5
“See Rosenbaum (2010); Yang et al. (2012); Yu and Rosenbaum (2019); Rosenbaum (2012) for details.”
BackgroundInfluentialChen, Z., Li, X., & Zhang, B. (2024) · Statistical Communications in Infectious Diseases · doi:10.1515/scid-2024-0001 · Cited by 4
“Many methods can be used to perform covariance adjustment; in early phase trials with small samples, one reasonable strategy is to conduct a matched cohort study (Rosenbaum, 2002, 2010).”
MethodDouble machine learning methods for estimating average treatment effects: a comparative study
Tan, X., Yang, S., Ye, W., Faries, D. E., Lipkovich, I. A., & KADZIOLA, Z. A. (2025) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2025.2489281 · Cited by 4
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An Exact Test of Fit for the Gaussian Linear Model Using Optimal Nonbipartite Matching
Pimentel, S. D., Small, D. S., & Rosenbaum, P. R. (2016) · Technometrics · doi:10.1080/00401706.2016.1212737 · Cited by 4
Self-citationBagged one‐to‐one matching for efficient and robust treatment effect estimation
Samuels, L. R., & Greevy, R. A. (2018) · Statistics in Medicine · doi:10.1002/sim.7926 · Cited by 4
Comparing Values of Manufactured and Equivalent Site-Built Homes in the Rural United States
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A hierarchical algorithm for multicentric matched cohort study designs
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Pre-analysis Plan for a Comparison of Matching and Black Box-based Covariate Adjustment
Keele, L. J., & Small, D. S. (2018) · Observational Studies · doi:10.1353/obs.2018.0017 · Cited by 4
“Examples of such refinements include optimal subset matching (Rosenbaum, 2012), almost exact matching (Rosenbaum, 2010), methods for fine and near-fine balance (Rosenbaum et al., 2007; Yang et al., 2012), near-far matching (Lu et al., 2001), covariate balance prioritization (Zubizarreta, 2012;…”
MethodBlack, B. S., & Kim, H. K. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1641459 · Cited by 5
Exact P-values for Network InterferencePreprint
Athey, S. C., Eckles, D., & Imbens, G. W. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.02084 · Cited by 4
Offline Experiences and Value Creation in Omnichannel RetailPreprint
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How Judicial Identity Changes the Text of Legal RulingsPreprint
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Flexible template matching for observational study design
Zhao, R., & Lü, B. (2023) · Statistics in Medicine · doi:10.1002/sim.9698 · Cited by 3
“(4) As a design tool, it leaves analytical options open for post-matching inference, from randomization-based nonparametric tests (more robust) to various regression analyses (more efficient).”
Graphical causal modelling: an application to identify and estimate cause-and-effect relationships
Burnett, J. W., & Blackwell, C. (2023) · Applied Economics · doi:10.1080/00036846.2023.2208856 · Cited by 3
Covariate-Balancing-Aware Interpretable Deep Learning Models for Treatment Effect Estimation
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“In causal inference, observational data refers to the information obtained from a sample or population that independent variables cannot be controlled over by the researchers because of ethical concerns or logistical constraints [1].”
Developing reading fluency in primary school: evidence from an RCT
Gomes, M., & Hirata, G. (2024) · Education Economics · doi:10.1080/09645292.2024.2322535 · Cited by 6
“Since our study relies on data from an RCT, we use randomization inference (Imbens and Rubin 2015; Rosenbaum 2010) as the main approach to inference analysis.”
A brief and general overview of quantitative designs for pediatric nurses
Azar, N. G., Eisen, A. M., Rahman, H. Q. A., Alrimawi, I., Vaughn, K., Patton, L. J., Ellis, K. K., & Taha, A. A. (2024) · Journal of Pediatric Nursing · doi:10.1016/j.pedn.2024.08.010 · Cited by 3
Gender differences in sleep behaviors under China’s universal two-child policy
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Sensitivity Analysis for Quantiles of Hidden Biases in Matched Observational Studies
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“Various approaches have been proposed to adjust for covariate imbalance between different treatment groups (see, e.g., Rosenbaum 2010; Imbens and Rubin 2015; Hernán and Robins 2020).”
Business group affiliation and misreporting: evidence from Korean chaebols
Ahn, J. H., Shah, S. Z. A., & Imam, S. (2025) · Accounting and Business Research · doi:10.1080/00014788.2025.2488927 · Cited by 3
Robust Inferences from a Before-and-After Study with Multiple Unaffected Control Groups
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Black Candidates and Black Turnout: A Study of Mayoral Elections in the New South∗
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Targeted temperature management in cardiac arrest: survival evaluated by propensity score matching
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Improving Computer Science Education through Cloud Computing: An Observational Study
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Interpreting the effectiveness of a summer reading program: The eye of the beholder
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Improving Outcomes of Underrepresented College Students Through Community-Engaged Employment
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Content-based Stock Recommendation Using Smartphone Data
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Treatment Effect Performance of the X-Learner in the Presence of Confounding and Non-Linearity
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Prop, L. J. C., van der Laan, A. M., Beerthuizen, M. G. C. J., Barendregt, C. S., & van Nieuwenhuizen, C. (2023) · Journal of Experimental Criminology · doi:10.1007/s11292-023-09593-7 · Cited by 5
“However, in exact matching, it is often challenging to find an exact match for all covariates, which may lead to high drop-out rates (Rosenbaum, 2010).”
Asl, E. M., Saghafipour, A., Hamta, A., Taheri‐Kharameh, Z., Abazari, M., & Jajin, S. A. (2024) · BMC Infectious Diseases · doi:10.1186/s12879-024-09029-1 · Cited by 3
“In this study, PSM was used to balance the distribution of covariates between the intervention and control groups, since random assignment was not possible [11, 12]..”
MethodCausation, Comparison, and Regression
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Does membership of the EMU matter for economic and financial outcomes?
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Protocols for Observational Studies: Methods and Open Problems
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Peaceful and Violent Origins of Voting Rights
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Impact of Protected Areas on Forests in Madagascar
Gimenez, T. G. (2012) · Cited by 3
Rank tests in unmatched clustered randomized trials applied to a study of teacher training
Ding, P., & Keele, L. J. (2018) · The Annals of Applied Statistics · doi:10.1214/18-aoas1147 · Cited by 3
“Although Neyman (1935)’s early analysis of experiments incorporated additive “technical errors” in the potential outcomes, they have been viewed as nuisances in randomization-based causal inference and have often been ignored (Rosenbaum 2010; Imbens and Rubin 2015).”
MethodLarge Sample Properties of Matching for Balance
Wang, Z., & Zubizarreta, J. R. (2021) · Statistica Sinica · doi:10.5705/ss.202020.0343 · Cited by 3
An exact test with high power and robustness to unmeasured confounding effects
Shauly‐Aharonov, M. (2020) · Statistics in Medicine · doi:10.1002/sim.8460 · Cited by 3
“The sensitivity model given in Equations (1) and (2) is applicable to a diverse range of circumstances, including binary outcomes and censored survival times.8 However, it is not the only model that can be applied in omitted-variable sensitivity analyses.”
BackgroundInfluentialLiu, Y., Kim, C., Wu, A. D., Gustafson, P., Kroc, E., & Zumbo, B. D. (2020) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1556669280 · Cited by 3
“…score methods can help to balance the characteristics of non-equivalent groups, so that two subgroups with the same propensity score values have the same distribution on observed covariates (e.g., Rosenbaum, 1995, 2002, 2010; Rosenbaum & Rubin, 1983, 1985; Rubin, 2001; Schafer & Kang, 2008).”
BackgroundPiccone, J. E. (2015) · NSUWorks (Nova Southeastern University) · Cited by 3
Rotar, L. J. (2012) · South East European Journal of Economics and Business · doi:10.2478/v10033-012-0004-8 · Cited by 3
Statistics and International Security
Lauretig, A., & Braumoeller, B. F. (2018) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780198777854.013.10 · Cited by 3
White, M., Rowan, B., Hansen, B. B., & Lycurgus, T. (2019) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2019.1636438 · Cited by 3
“We could use a risk set matching approach to match each BURST school with schools in the population frame in their risk set within a specified caliper (see Rosenbaum, 2009).”
Methodvan den Bogaart, E. H. A., Spreeuwenberg, M. D., Kroese, M., van Hoof, S. J. M., Hameleers, N., & Ruwaard, D. (2020) · Journal of Evaluation in Clinical Practice · doi:10.1111/jep.13426 · Cited by 3
“To correct for this potential selection bias, which may affect the estimates of the treatment effect, PSM was used.(35) First, the propensity score (PS) was estimated using logistic regression, which predicts the likelihood of a referral to PC+ or HBOC based on the baseline characteristics described earlier.”
MethodLearning Causal Effect Using Machine Learning with Application to China’s Typhoon
Wu, P., Hu, Q., Tong, X., & Wu, M. (2020) · Acta Mathematicae Applicatae Sinica English Series · doi:10.1007/s10255-020-0960-1 · Cited by 3
Zhai, R., & Gutman, R. (2021) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2021.1946806 · Cited by 3
Instrumental Variable Analysis
Baiocchi, M., Cheng, J., & Small, D. S. (2019) · Health services research · doi:10.1007/978-1-4939-8715-3_32 · Cited by 3
Overlap Violations in Clustered Observational Studies of Educational Interventions
Keele, L. J., Lenard, M., & Page, L. C. (2022) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2022.2144563 · Cited by 3
“The literature suggests that the standardized difference should be < 0.20 (Ho et al., 2007; Stuart, 2010), though a more stringent criterion of 0.10 is suggested by others (Mamdani et al., 2005; Rosenbaum, 2010).”
BackgroundInfluentialEfficient Algorithms for Building Representative Matched Pairs with Enhanced Generalizability
Zhang, B. (2023) · Biometrics · doi:10.1111/biom.13919 · Cited by 3
“Compared to MIP-based methods, network-flow-based methods only require solving a polynomial solvable problem that is tractable both in theory and practice and have proven successful in empirical comparative effectiveness research for decades (Rosenbaum, 2002, 2010; Stuart, 2010).”
MethodInfluentialBook Review Feature: Public Policy in an Uncertain World
Imbens, G. W. (2013) · The Economic Journal · doi:10.1111/ecoj.12065 · Cited by 3
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Forced to Fight: Coercion, Blocking Detachments, and Tradeoffs in Military EffectivenessPreprint
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Raising the bar for reading comprehension
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The Impact of Stakeholder Orientation on Bank Risk-Taking: Evidence from Natural ExperimentPreprint
Leung, W. S., Song, W., & Chen, J. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2668126 · Cited by 3
Discovering Effect Modification and Randomization Inference in Air Pollution StudiesPreprint
Lee, K., Small, D. S., & Dominici, F. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1802.06710 · Cited by 3
Demirkaya, E., Fan, Y., Gao, L., Lv, J., Vossler, P., & Wang, J. (2018) · arXiv (Cornell University) · Cited by 3
Causal Bias Quantification for Continuous Treatment.Preprint
Detommaso, G., Brückner, M., Schulz, P., & Chernozhukov, V. (2021) · arXiv (Cornell University) · Cited by 3
Observational Studies: Overview
Rosenbaum, P. R. (2015) · Elsevier eBooks · doi:10.1016/b978-0-08-097086-8.42159-8 · Cited by 3
Self-citation
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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