| Interpreting relative risks and odds ratios after propensity score matching: practical guidance for clinical research |
Jonghae Kim1 
, Boohwi Hong2
, Dong-Kyu Lee3
, EunJin Ahn4
, Hye Jin Kim5
, Hyun Kang4
, Junyong In6
, Sangseok Lee7
, Sang Gyu Kwak8
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1Department of Anesthesiology and Pain Medicine, Daegu Catholic University School of Medicine, Daegu, Korea
2Department of Anesthesiology and Pain Medicine, Chungnam National University Hospital, College of Medicine, Chungnam National University, Daejeon, Korea
3Department of Anesthesiology and Pain Medicine, Dongguk University Ilsan Hospital, Goyang, Korea
4Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Medicine, Seoul, Korea
5Department of Anesthesiology and Pain Medicine, Anesthesia and Pain Research Institute, Yonsei University College of Medicine, Seoul, Korea
6Department of Anesthesiology and Pain Medicine, Dongguk University Ilsan Hospital, Goyang, Korea
7Department of Anesthesiology and Pain Medicine, Sanggye Paik Hospital, Inje University College of Medicine, Seoul, Korea
8Department of Medical Statistics, Daegu Catholic University School of Medicine, Daegu, Korea |
Corresponding author:
Sang Gyu Kwak, Tel: +82-53-650-4724, Fax: +82-53-621-4106,
Email: sgkwak@cu.ac.kr
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Received: 27 October 2025 • Revised: 24 March 2026 • Accepted: 1 April 2026 |
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| Abstract |
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In observational studies, using relative risks (RRs) or odds ratios (ORs) influences the interpretation and generalizability of results, particularly after propensity-score matching (PSM). Here, we explain the theoretical and practical differences between the RR and OR across varying event probabilities and examine the influence of PSM. We illustrate the behaviors of the RR, OR, and their ratios mathematically and graphically across event probabilities. Using a simulated dataset with a binary outcome and three covariates (age, sex, and Body Mass Index), we demonstrate how PSM can change event rates, RRs, ORs, and RR collapsibility. The OR departs from unity more steeply than does the RR as the event probabilities diverge, whereas both measures converge for probabilities below 0.10. When groups have similar event probabilities, the OR and RR diverge minimally, even at high probabilities. PSM shifts the covariate distributions and alters the event rates, RRs, and ORs. The discrepancies between the RR and OR widens when event rates exceed 0.10, but remain small at lower rates. The weighted averages of sex-specific RRs closely approximate the marginal RR, illustrating RR collapse. Interpreting the RR and OR after PSM requires caution. While the OR may overestimate or underestimate associations, depending on the event rates, the RR is generally suitable as a marginal measure, but PSM modifies the study population, making the matched sample a product of statistical modeling. Reporting ORs after PSM is generally appropriate, but cross-checking with a collapsible measure, such as the marginal RR, can help to evaluate effect estimate robustness. |
| Key Words:
Cohort study; Incidence; Odds ratio; Probability; Propensity score; Relative risk |
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