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

Area of Science:

• Causal Inference
• Bayesian Confirmation Theory
• Semantic Information

Background:

• Simpson's Paradox presents a contradiction where aggregated data shows a different trend than individual subgroups.
• Existing Causal Inference Theory (ECIT) attempts to resolve this by removing confounder influence, using relative risk difference (P) as probability of causation.
• Philosopher Fitelson's Bayesian confirmation measure (D) suggests accepting overall conclusions without addressing the paradox.

Purpose of the Study:

• To reconcile the contradiction between ECIT and Bayesian confirmation regarding Simpson's Paradox.
• To propose a novel causal confirmation measure (Cc) that addresses the limitations of existing methods.

Main Methods:

• Utilized the semantic information method with the minimum cross-entropy criterion.
• Developed a new causal confirmation measure, Cc = (R - 1)/max(R, 1), where R is the risk ratio.
• Compared Cc with existing measures (P and D) using examples like kidney stone treatments and COVID-19 data.

Main Results:

• The proposed causal confirmation measure (Cc) possesses normalizing properties (ranging from -1 to 1) and cause symmetry.
• Cc is particularly effective in scenarios where a cause restrains an outcome, such as vaccine efficacy in controlling infections.
• Empirical examples demonstrated that both P and Cc are more reasonable than D, with Cc showing greater utility than P.

Conclusions:

• The novel causal confirmation measure (Cc) effectively overcomes the paradoxes presented by Simpson's Paradox.
• Cc offers a more robust and versatile approach to measuring causal strength compared to existing methods.
• The findings suggest Cc is a valuable tool for causal inference, especially in public health and medical research.