An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies
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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.
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The study used an active comparator, new-user design with propensity score matching that adjusted for baseline use of other antidiabetic drugs to minimize confounding by cotreatment.
“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]
The sections on propensity score matching and variable selection explain matching on propensity scores and including measured baseline covariates to address confounding (page numbers unavailable). They do not describe the citing study, an active-comparator new-user design, or adjustment for other antidiabetic drugs to minimize confounding by cotreatment. (LLM, conf=0.87)
Experimental — accuracy not yet measuredThe impact of implementation was evaluated using propensity score matching to account for potential confounding factors.
“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]
Propensity score matching is considered a robust method.
“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
Propensity score matching is an analytic approach to reduce bias of measured confounding effects.
“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
Statistical models for confounding adjustment, including propensity scores and inverse probability weighting, rely on the assumption of no unmeasured confounding for the validity of the effect estimate.
“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 cohort studies, influenza vaccination was associated not only with protection against hospitalisation for pneumonia but also against hospitalisation for injury or trauma, indicating that the beneficial effect on pneumonia may have been overestimated.
“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]
Each of the four principal ways to use the propensity score to obtain an estimated treatment effect-matching, stratification, inverse probability weighting, and covariate adjustment-will adjust for differences in characteristics of the intervention and control groups and, in so doing, minimize the effects of confounding.
“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]
The active comparator design adjusted for confounding from all factors shared across individuals initiating analgesic treatment with opioids and with NSAIDs.
“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]
The active comparator design cannot account for unmeasured factors that differentiate opioid and NSAID initiators.
“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]
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“Ideally, propensity-score matching should be used, which allows to analyze life event data so that it mimics features of randomized controlled trials and thereby reduces the effects of confounding factors (Austin, 2011).”
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- 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
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