Causal Confirmation Measures: From Simpson’s Paradox to COVID-19. (arXiv:2302.09067v1 [cs.AI])

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 Pd = max(0, (R – 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
-1)/max(R, 1). Cc is like Pd 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 Pd and Cc are more
reasonable than D; Cc is more useful than Pd.