Causal Confirmation Measures: From Simpson's Paradox to COVID-19

• Published in: Entropy (Basel, Switzerland) Switzerland), 2023-01, Vol.25 (1), p.143
• Main Author: Lu, Chenguang
• Format: Article
• Language: English
• Subjects: Age groups; Bayesian analysis; Bayesian confirmation; Bias; Blood pressure; Calculi; causal confirmation; causal inference; Causality; Causation; Conditional probability; Coronaviruses; COVID-19; cross-entropy; Entropy (Information theory); Fatalities; Hispanic people; Hypotheses; Medical tests; Paradoxes; semantic information measure; Simpson’s Paradox; Success; Symmetry
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25010143

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's Paradox. The Existing Causal Inference Theory (ECIT) can make the overall conclusion consistent with the grouping conclusion by removing the confounder's influence to eliminate the paradox. The ECIT uses relative risk difference = max(0, ( - 1)/ ) ( denotes the risk ratio) as the probability of causation. In contrast, Philosopher Fitelson uses confirmation measure (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 * similar to 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 = ( - 1)/max( , 1). is like but has normalizing property (between -1 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 and are more reasonable than ; is more useful than .