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

TL;DR

This paper introduces a new causal confirmation measure Cc, based on Bayesian principles and semantic information, which addresses limitations of existing measures like Pd and D, especially in cases like COVID-19 control.

Contribution

The paper proposes the Cc measure that normalizes causal confirmation, resolving contradictions between existing measures and enhancing causal inference in complex scenarios.

Findings

Cc is more reasonable than D and Pd in examples

Cc has normalization and cause symmetry properties

Examples demonstrate Cc's effectiveness in COVID-19 and kidney stone cases

Abstract

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.