{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T14:15:58Z","timestamp":1772720158353,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T00:00:00Z","timestamp":1673308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>When we compare the influences of two causes on an outcome, if the conclusion from every group is against that from the conflation, we think there is Simpson\u2019s Paradox. The Existing Causal Inference Theory (ECIT) can make the overall conclusion consistent with the grouping conclusion by removing the confounder\u2019s influence to eliminate the paradox. The ECIT uses relative risk difference Pd = max(0, (R \u2212 1)\/R) (R denotes the risk ratio) as the probability of causation. In contrast, Philosopher Fitelson uses confirmation measure D (posterior probability minus prior probability) to measure the strength of causation. Fitelson concludes that from the perspective of Bayesian confirmation, we should directly accept the overall conclusion without considering the paradox. The author proposed a Bayesian confirmation measure b* similar to Pd before. To overcome the contradiction between the ECIT and Bayesian confirmation, the author uses the semantic information method with the minimum cross-entropy criterion to deduce causal confirmation measure Cc = (R \u2212 1)\/max(R, 1). Cc is like Pd but has normalizing property (between \u22121 and 1) and cause symmetry. It especially fits cases where a cause restrains an outcome, such as the COVID-19 vaccine controlling the infection. Some examples (about kidney stone treatments and COVID-19) reveal that Pd and Cc are more reasonable than D; Cc is more useful than Pd.<\/jats:p>","DOI":"10.3390\/e25010143","type":"journal-article","created":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T02:06:03Z","timestamp":1673402763000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Causal Confirmation Measures: From Simpson\u2019s Paradox to COVID-19"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8669-0094","authenticated-orcid":false,"given":"Chenguang","family":"Lu","sequence":"first","affiliation":[{"name":"Intelligence Engineering and Mathematics Institute, Liaoning Technical University, Fuxin 123000, China"},{"name":"School of Computer Engineering and Applied Mathematics, Changsha University, Changsha 410022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1198\/016214504000001880","article-title":"Causal inference using potential outcomes","volume":"100","author":"Rubin","year":"2005","journal-title":"J. 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