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Similarly, this parameterization of a linear additive risk-ratio model allows us to construct the confidence intervals of α i ( i = 0, 1, 2, 3) by profile likelihood. RERI (the relative excess risk due to interaction 1) is defined as:įurther, the coefficient α 3 measures the departure of exposure effect from additivity on a risk-ratio scale that is, the relative excess risk due to interaction (RERI). Let the quantity RR and OR denote the risk ratio and odds ratio, respectively. METHODS Background and Definitions of the Relative Excess Risk due to InteractionĪfter the notation of Hosmer and Lemeshow, 1 we let A and B denote the presence of 2 binary risk factors, and Ā and denote their absence. To the best of our knowledge, Bayesian methods have not previously been applied to the estimation of RERIs. Frequentist approaches for the estimation of additive interaction and associated confidence limits have recently been proffered by Zou, 4 Richardson and Kaufman, 5 Nie et al, 6 and others 7,8 as an alternative, we describe a Bayesian approach to the estimation of the RERI. 1–3 This measure is sometimes used in epidemiologic studies of the joint effects of 2 binary exposures on disease risk. The relative excess risk due to interaction (RERI), also referred to as the interaction contrast ratio, is defined as a departure from additivity of effects on a relative-risk scale.
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