The DOI matches its Crossref record; 95 of the 95 references it cites were found in a registry or an index.
An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies
Open accessAbstract
The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The study maintained an active comparator, new-user design, with propensity score matching that adjusted for baseline use of other antidiabetic drugs to minimize confounding by cotreatment.39”
From Neurodegeneration and Stroke After Semaglutide and Tirzepatide in Patients With Diabetes and Obesity (2025) · cites this paper as [39]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“The impact of this implementation was evaluated by comparing clinical outcomes before and after system deployment, using propensity score matching to account for potential confounding factors43.”
From Machine learning predicts sepsis deterioration trajectories. (2026) · cites this paper as [43]
The cited source says what the claim attributes to it.
In the citing paper
“PSM is considered a robust method (Austin, 2011; Benedetto et al., 2018).”
From Midwifery continuity of care, breastfeeding and neonatal hyperbilirubinemia: A retrospective cohort study (2024) · cites this paper as Austin, 2011
The cited source says what the claim attributes to it.
In the citing paper
“PSM is an analytic approach to reduce bias of measured confounding effects from covariates (Austin, 2011; Benedetto et al., 2018).”
From Midwifery continuity of care, breastfeeding and neonatal hyperbilirubinemia: A retrospective cohort study (2024) · cites this paper as Austin, 2011
In the citing paper
“All of these models, including more advanced techniques such as propensity scores [46] or inverse probability weighting, rely on the assumption of no unmeasured confounding for the validity of the effect estimate.”
From COSMOS-E: Guidance on conducting systematic reviews and meta-analyses of observational studies of etiology (2019) · cites this paper as [46]
In the citing paper
“Similarly, in cohort studies, vaccination against influenza not only protected against hospitalisation for pneumonia but also against hospitalisation for injury or trauma [46], indicating that the beneficial effect on pneumonia may have been overestimated.”
From COSMOS-E: Guidance on conducting systematic reviews and meta-analyses of observational studies of etiology (2019) · cites this paper as [46]
In the citing paper
“There are four principal ways to use the propensity score to obtain an estimated treatment effect: matching, stratification, inverse probability weighting, and covariate adjustment (7). Each method will adjust for differences in characteristics of the intervention and control groups and, in so doing, minimize the effects of confounding.”
From Natural Experiments: An Overview of Methods, Approaches, and Contributions to Public Health Intervention Research (2017) · cites this paper as [7]
In the citing paper
“This approach adjusted for confounding from all factors shared across individuals initiating analgesic treatment with opioids and with NSAIDs (eg, indications for pain treatment)”
From Association of opioid prescription initiation during adolescence and young adulthood with subsequent substance-related morbidity (2020) · cites this paper as [42]
In the citing paper
“The active comparator design cannot account for unmeasured factors that differentiate opioid and NSAID initiators”
From Association of opioid prescription initiation during adolescence and young adulthood with subsequent substance-related morbidity (2020) · cites this paper as [42]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The central role of the propensity score in observational studies for causal effects
ROSENBAUM, P. R., & RUBIN, D. B. (1983) · Biometrika · doi:10.1093/biomet/70.1.41 · Cited by 31,241
A simulation study of the number of events per variable in logistic regression analysis
Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(96)00236-3 · Cited by 9,655
Estimating causal effects of treatments in randomized and nonrandomized studies
Rubin, D. B. (1974) · Journal of Educational Psychology · doi:10.1037/h0037350 · Cited by 9,436
Austin, P. C. (2009) · Statistics in Medicine · doi:10.1002/sim.3697 · Cited by 6,758
Self-citationRosenbaum, P. R., & Rubin, D. B. (1985) · The American Statistician · doi:10.2307/2683903 · Cited by 6,472
Marginal Structural Models and Causal Inference in Epidemiology
Robins, J. M., Hernán, M. Á., & Brumback, B. (2000) · Epidemiology · doi:10.1097/00001648-200009000-00011 · Cited by 5,581
MatchIt : Nonparametric Preprocessing for Parametric Causal Inference
Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2011) · Journal of Statistical Software · doi:10.18637/jss.v042.i08 · Cited by 4,385
Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference
Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2007) · Political Analysis · doi:10.1093/pan/mpl013 · Cited by 4,285
Austin, P. C. (2011) · Pharmaceutical Statistics · doi:10.1002/pst.433 · Cited by 3,949
Self-citationCausal Diagrams for Epidemiologic Research
Greenland, S., Pearl, J., & Robins, J. M. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00008 · Cited by 3,728
Cited by
Sorted by citations
Items 101–144 of 144
Davies, S. J., Rudoler, D., de Oliveira, C., Huang, A., Kurdyak, P., & Iaboni, A. (2022) · Journal of Psychopharmacology · doi:10.1177/02698811211069096 · Cited by 32
Chang, K.-C., Shao, S.-C., Kuo, S., Yang, C.-Y., Chen, H.-Y., Chan, Y.-Y., & Ou, H.-T. (2020) · Cardiovascular Diabetology · doi:10.1186/s12933-020-01148-8 · Cited by 28
Grodecki, K., Tamarappoo, B. K., Huczek, Z., Jedrzejczyk, S., Cadet, S., Kwiecinski, J., Rymuza, B., Parma, R., Olasinska-Wisniewska, A., Fijalkowska, J., et al. (2021) · European Heart Journal - Cardiovascular Imaging · doi:10.1093/ehjci/jeaa304 · Cited by 38
El Baou, C., Bell, G., Saunders, R., Buckman, J. E. J., Mandy, W., Dagnan, D., O'Nions, E., Pender, R., Clements, H., Pilling, S., et al. (2023) · The Lancet Psychiatry · doi:10.1016/s2215-0366(23)00291-2 · Cited by 37
“…for clinical and sociodemographic covariates; (3) additionally adjusted for IAPT treatment factors; and (4) rerun using a propensity score matched 28 sample to account for differences between the autistic group and the comparison group, and as recommended when the size of the comparison group…”
Joo, J. H., Sharma, N., Shaia, J., Wu, A. K., Skugor, M., Singh, R. P., & Rachitskaya, A. V. (2024) · Ophthalmology Science · doi:10.1016/j.xops.2024.100547 · Cited by 37
Kiratipaisarl, W., Surawattanasakul, V., & Sirikul, W. (2024) · BMC Medical Education · doi:10.1186/s12909-024-06195-3 · Cited by 37
“Randomized studies, such as preference-based trials [99], and non-randomized studies with targeted trial frameworks, incorporating adequate baseline and time-varying confounder control methods like regression and inverse probability weighting can enhance the effectiveness of outcomes [34, 100, 101].”
Backgroundvan Rosendael, P. J., Kamperidis, V., Kong, W. K. F., van Rosendael, A. R., Marsan, N. A., Bax, J. J., & Delgado, V. (2016) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2016.08.021 · Cited by 34
Eakman, A. M., Schelly, C., & Henry, K. L. (2016) · American Journal of Occupational Therapy · doi:10.5014/ajot.2016.016519 · Cited by 35
Upper Airway Stimulation vs Positive Airway Pressure Impact on BP and Sleepiness Symptoms in OSA
Walia, H. K., Thompson, N. R., Strohl, K. P., Faulx, M. D., Waters, T., Kominsky, A., Foldvary-Schaefer, N., & Mehra, R. (2020) · Chest · doi:10.1016/j.chest.2019.06.020 · Cited by 34
Hong, B., Bea, S., Ko, H. Y., Kim, W. J., Cho, Y. M., & Shin, J.-Y. (2024) · Annals of Internal Medicine · doi:10.7326/m23-3220 · Cited by 33
Chen, J. (2024) · System · doi:10.1016/j.system.2024.103388 · Cited by 33
Approaches to addressing missing values, measurement error, and confounding in epidemiologic studies
van Smeden, M., Penning de Vries, B. B. L., Nab, L., & Groenwold, R. H. H. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2020.11.006 · Cited by 32
Thomsen, C. T., Benros, M. E., Maltesen, T., Hastrup, L. H., Andersen, P. K., Giacco, D., & Nordentoft, M. (2018) · Acta Psychiatrica Scandinavica · doi:10.1111/acps.12868 · Cited by 32
Kałużna, M., Czlapka-Matyasik, M., Kompf, P., Moczko, J., Wachowiak-Ochmańska, K., Janicki, A., Samarzewska, K., Ruchała, M., & Ziemnicka, K. (2022) · Therapeutic Advances in Endocrinology and Metabolism · doi:10.1177/20420188211066699 · Cited by 32
Hogan, M.-E., Taddio, A., Katz, J., Shah, V., & Krahn, M. (2017) · Pain · doi:10.1097/j.pain.0000000000000776 · Cited by 30
Webb, S. J., Garrison, M. M., Bernier, R., McClintic, A. M., King, B. H., & Mourad, P. D. (2017) · Autism Research · doi:10.1002/aur.1690 · Cited by 29
Takiguchi, T., Nakajima, M., Ohbe, H., Sasabuchi, Y., Matsui, H., Fushimi, K., Kim, S., Yokota, H., & Yasunaga, H. (2020) · Critical Care Medicine · doi:10.1097/ccm.0000000000004255 · Cited by 28
Finnerty, M. T., Layman, D. M., Chen, Q., Leckman-Westin, E., Bermeo, N., Ng-Mak, D. S., Rajagopalan, K., & Hoagwood, K. E. (2018) · Psychiatric Services · doi:10.1176/appi.ps.201800130 · Cited by 28
Chien, Y.-L., Lin, H.-Y., Tung, Y.-H., Hwang, T.-J., Chen, C.-L., Wu, C.-S., Shang, C.-Y., Hwu, H.-G., Tseng, W.-Y. I., Liu, C.-M., et al. (2022) · Molecular Psychiatry · doi:10.1038/s41380-022-01636-1 · Cited by 24
Challenges and Solutions to Pre- and Post-Randomization Subgroup Analyses
Desai, M., Pieper, K. S., & Mahaffey, K. (2014) · Current Cardiology Reports · doi:10.1007/s11886-014-0531-2 · Cited by 26
Clinical efficacy of pre-trained large language models through the lens of aphasia
Cong, Y., LaCroix, A. N., & Lee, J. (2024) · Scientific Reports · doi:10.1038/s41598-024-66576-y · Cited by 25
“Considering the sample size, we specified the method parameter as “nearest” to implement nearest neighbor matching, using a logistic (probit) regression propensity score 54 .”
MethodClifasefi, S. L., Collins, S. E., & The LEAP Advisory Board (2020) · Journal of Community Psychology · doi:10.1002/jcop.22291 · Cited by 23
The antidepressant standoff: Why it continues and how to resolve it
Ormel, J., Spinhoven, P., de Vries, Y. A., Cramer, A. O. J., Siegle, G. J., Bockting, C. L. H., & Hollon, S. D. (2020) · Psychological Medicine · doi:10.1017/s0033291719003295 · Cited by 22
Using Aggregate Patient Data at the Bedside via an On-Demand Consultation Service
Callahan, A., Gombar, S., Cahan, E. M., Jung, K., Steinberg, E., Polony, V., Morse, K., Tibshirani, R., Hastie, T., Harrington, R., et al. (2021) · NEJM Catalyst · doi:10.1056/cat.21.0224 · Cited by 24
Yoshida, K., Yu, Z., Greendale, G. A., Ruppert, K., Lian, Y., Tedeschi, S. K., Lin, T., Haneuse, S., Glynn, R. J., Hernández‐Díaz, S., et al. (2018) · Pharmacoepidemiology and Drug Safety · doi:10.1002/pds.4362 · Cited by 18
Lee, T., Kuo, S., Yang, C., & Ou, H. (2020) · British Journal of Clinical Pharmacology · doi:10.1111/bcp.14188 · Cited by 18
Impact of compulsory admission on treatment and outcome: A propensity score matched analysis
Hofmann, A. B., Schmid, H. M., Hofmann, L. A., Noboa, V., Seifritz, E., Vetter, S., & Egger, S. T. (2022) · European Psychiatry · doi:10.1192/j.eurpsy.2022.4 · Cited by 19
Pan, K., Li, R., Li, Y., Ding, X., Li, X., & Lv, Q. (2025) · Journal of Antimicrobial Chemotherapy · doi:10.1093/jac/dkae410 · Cited by 16
Dong, Y., Wu, J., Chang, C., Lin, J., Wu, L., & Toh, S. (2022) · Pharmacotherapy: The Journal of Human Pharmacology and Drug Therapy · doi:10.1002/phar.2688 · Cited by 16
McIntyre, R. S., Prieto, R., Schepman, P., Yeh, Y.-C., Boucher, M., Shelbaya, A., Chambers, R., Gao, X., & Pappadopulos, E. (2019) · Current Medical Research and Opinion · doi:10.1080/03007995.2019.1652053 · Cited by 15
Can We Establish Causality with Statistical Analyses? The Example of Epidemiology
Frick, U., & Rehm, J. (2016) · Wiley Series in Probability and Statistics · doi:10.1002/9781118947074.ch17 · Cited by 14
Trinh, M., Khou, V., Kalloniatis, M., & Nivison-Smith, L. (2021) · Investigative Opthalmology & Visual Science · doi:10.1167/iovs.62.13.13 · Cited by 14
Margolis, J. M., Deitelzweig, S., Kline, J., Tran, O., Smith, D. M., Crivera, C., Bookhart, B., & Schein, J. (2016) · Clinical Therapeutics · doi:10.1016/j.clinthera.2016.09.007 · Cited by 13
Antibiotic De-escalation in adults hospitalized for community-onset Sepsis
Gupta, A. B., Heath, M., Walzl, E., Ratz, D., Munroe, E., Vaughn, V. M., Horowitz, J. K., Czilok, T., Petty, L. A., Gandhi, T. N., et al. (2026) · JAMA Internal Medicine · doi:10.1001/jamainternmed.2025.6919 · Cited by 14
Bottigliengo, D., Lorenzoni, G., Ocagli, H., Martinato, M., Berchialla, P., & Gregori, D. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18136694 · Cited by 13
Impact of Dementia on Long-Term Hip Fracture Surgery Outcomes: An Electronic Health Record Analysis
Xue, T. (., Pan, W., Tsumura, H., Wei, S., Lee, C., & McConnell, E. S. (2023) · Journal of the American Medical Directors Association · doi:10.1016/j.jamda.2022.11.006 · Cited by 12
AI Companions Reduce Loneliness
De Freitas, J., Uguralp, A. K., Uguralp, Z. O., & Stefano, P. (2024) · arXiv · doi:10.48550/arxiv.2407.19096 · Cited by 12
Haji Ali Afzali, H., Gray, J., Beilby, J., Holton, C., & Karnon, J. (2013) · Applied Health Economics and Health Policy · doi:10.1007/s40258-013-0062-9 · Cited by 10
Yamakawa, S., Nagayama, H., Tomori, K., Ikeda, K., & Niimi, A. (2023) · Frontiers in Rehabilitation Sciences · doi:10.3389/fresc.2022.1045231 · Cited by 10
Smith, D. C., Reinhart, C. A., Begum, S., Kosgolla, J., Kelly, J. F., Bergman, B. B., & Basic, M. (2023) · PLoS ONE · doi:10.1371/journal.pone.0295330 · Cited by 9
Lee, J. L., Billovits, C., Chen, S.-Y., Wickham, R. E., Kocher, B., Chen, C. E., & Lungu, A. (2025) · Value in Health · doi:10.1016/j.jval.2025.06.002 · Cited by 8
Shahshahani, M. A., Liu, X., Norman, M., Tilden, E. L., & Ahlberg, M. (2024) · Midwifery · doi:10.1016/j.midw.2024.104079 · Cited by 7
The effect of civilian oversight on police organizational performance: a quasi-experimental study
Kim, J. (2022) · The American Review of Public Administration · doi:10.1177/02750740221098344 · Cited by 7
Machine learning predicts sepsis deterioration trajectories.
Zhang, R., Long, F., Zhao, Z., Wu, J., Tan, R., Xu, W., Li, L., Long, Y., & Qu, H. (2026) · NPJ Digital Medicine · doi:10.1038/s41746-026-02565-x · Cited by 6
Metadata
- Authors
- Austin, P. C.
- Affiliations
- University of Toronto (CA)
- Corresponding author
- Austin, Peter C.
- ORCID
- Austin, Peter C.
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2011-05-31
- Volume
- 46
- Issue
- 3
- Pages
- 399-424
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- PMC
- PMC3144483
- OpenAlex
- W2036193982
- Cited by
- 12,242
- References
- 95
- Citations by year
- 2026: 1460 · 2025: 1302 · 2024: 1187 · 2023: 1145 · 2022: 1277 · 2021: 1253 · 2020: 1065 · 2019: 850 · 2018: 781 · 2017: 628 · 2016: 560 · 2015: 353 · 2014: 221 · 2013: 122 · 2012: 28
- FWCI
- 104.26
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Multivariate Behavioral Research (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Institute for Clinical Evaluative Sciences
- Ontario Ministry of Health and Long-Term Care
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- propensity score, confounding, observational studies, propensity score matching, stratification, inverse probability of treatment weighting, covariate adjustment, regression-based methods
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 ›
Are you an author, or do you see a problem with this page? Request a review
