The interpretation of multiplicative‐model parameters as standardized parameters

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Abstract
Under current conventions, relative-risk estimates obtained from multiplicative models are interpreted as estimates of a homogeneous, effect. Such interpretations condition on the unverifiable assumption that the relative risk under study is homogeneous, an assumption that is not likely to be correct even if the model fits well. We propose that such estimates are better interpreted as estimates of standardized relative risks, with a bias component that depends on the degree of model misspecification and on the study design. To evaluate our proposal, we present a study of the maximum-likelihood estimators from Poisson and logistic regression compared to the population-standardized rate ratio. The results indicate that our proposed interpretation would in practice be more cautious and accurate than the homogeneous-effect interpretation.