{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T19:00:21Z","timestamp":1764874821912,"version":"3.46.0"},"reference-count":10,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T00:00:00Z","timestamp":1764806400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of University and Research","award":["PRIN 2022 Grant (Prot. 202223XMAF; 3B4D)"],"award-info":[{"award-number":["PRIN 2022 Grant (Prot. 202223XMAF; 3B4D)"]}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:sec id=\"sec001\">\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Observational studies have consistently reported large reductions in COVID-19 risk among vaccinated individuals. However, critics have raised concerns that unmeasured confounding may entirely explain these associations.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec id=\"sec002\">\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We combined the classical Cornfield inequality with a Monte Carlo sensitivity analysis to evaluate whether unmeasured confounding alone could plausibly account for the observed effectiveness of COVID-19 vaccines. The Cornfield inequality provides a lower bound on the strength of confounding required to explain a given association. The Monte Carlo analysis simulates uncertainty over possible confounder\u2013exposure and confounder\u2013outcome relationships by drawing from weakly informative prior distributions, allowing us to estimate the frequency with which such confounding would be sufficient.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec id=\"sec003\">\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>For an observed risk ratio of 0.08\u2014consistent with early estimates for the Pfizer-BioNTech vaccine\u2014the confounder would need to be both highly imbalanced (e.g., 10 times more prevalent among vaccinated individuals) and strongly protective (e.g., reducing disease risk by 99%). Simulation results showed that, under the specified assumptions, fewer than 2% of draws satisfied this condition. Even in the more moderate case of a risk ratio of 0.25 (e.g., AstraZeneca), the proportion remained below 6%.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec id=\"sec004\">\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>Our findings suggest that while residual confounding may attenuate effect estimates, it is statistically and epidemiologically implausible that unmeasured confounding alone could fully account for the magnitude of observed vaccine effectiveness. This framework combines the falsificatory logic of Cornfield bounds with the flexibility of simulation-based sensitivity analysis, providing a transparent tool for evaluating confounding-based explanations in observational research.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1371\/journal.pone.0336063","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T18:54:30Z","timestamp":1764874470000},"page":"e0336063","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["The impossible confounder: Quantifying the limits of alternative explanations for COVID-19 vaccine effectiveness"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0822-862X","authenticated-orcid":true,"given":"Tommaso","family":"Costa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"issue":"8","key":"pone.0336063.ref001","article-title":"Why most published research findings are false","volume":"2","author":"JPA Ioannidis","year":"2005","journal-title":"PLoS Med"},{"issue":"5","key":"pone.0336063.ref002","first-page":"430","article-title":"Addressing the Challenges of Vaccine Hesitancy Broadly and Related to COVID-19 Vaccines","volume":"29","author":"MT Brown","year":"2022","journal-title":"Top Antivir Med"},{"issue":"2","key":"pone.0336063.ref003","first-page":"297","article-title":"Causation and the counterfactual","volume":"92","author":"PR Rosenbaum","year":"2005","journal-title":"Biometrika"},{"issue":"1","key":"pone.0336063.ref004","first-page":"173","article-title":"Smoking and lung cancer: recent evidence and a discussion of some questions","volume":"22","author":"J Cornfield","year":"1959","journal-title":"J Natl Cancer Inst"},{"issue":"15","key":"pone.0336063.ref005","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1056\/NEJMoa2101765","article-title":"BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Mass Vaccination Setting","volume":"384","author":"N Dagan","year":"2021","journal-title":"N Engl J Med"},{"issue":"4","key":"pone.0336063.ref006","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1056\/NEJMoa2107058","article-title":"Prevention and Attenuation of Covid-19 with the BNT162b2 and mRNA-1273 Vaccines","volume":"385","author":"MG Thompson","year":"2021","journal-title":"N Engl J Med"},{"issue":"10269","key":"pone.0336063.ref007","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0140-6736(20)32661-1","article-title":"Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK","volume":"397","author":"M Voysey","year":"2021","journal-title":"Lancet"},{"issue":"23","key":"pone.0336063.ref008","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1056\/NEJMoa2101544","article-title":"Safety and Efficacy of Single-Dose Ad26.COV2.S Vaccine against Covid-19","volume":"384","author":"J Sadoff","year":"2021","journal-title":"N Engl J Med"},{"issue":"4","key":"pone.0336063.ref009","doi-asserted-by":"crossref","first-page":"268","DOI":"10.7326\/M16-2607","article-title":"Sensitivity Analysis in Observational Research: Introducing the E-Value","volume":"167","author":"TJ VanderWeele","year":"2017","journal-title":"Ann Intern Med"},{"issue":"3","key":"pone.0336063.ref010","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1093\/oxfordjournals.aje.a008920","article-title":"Risk factors for osteoporotic fractures in elderly men","volume":"144","author":"TV Nguyen","year":"1996","journal-title":"Am J Epidemiol"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0336063","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T18:54:32Z","timestamp":1764874472000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0336063"}},"subtitle":[],"editor":[{"given":"Igor","family":"Burstyn","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,12,4]]},"references-count":10,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0336063","relation":{},"ISSN":["1932-6203"],"issn-type":[{"type":"electronic","value":"1932-6203"}],"subject":[],"published":{"date-parts":[[2025,12,4]]}}}