For any two outcome probabilities, the complementary log ratio approximates the risk ratio more closely than the odds ratio does, with a proof using the Aranda-Ordaz family of link functions.
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Improved Risk Ratio Approximation by Complementary Log-Log Models: A Comparison with Logistic Models
For any two outcome probabilities, the complementary log ratio approximates the risk ratio more closely than the odds ratio does, with a proof using the Aranda-Ordaz family of link functions.