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Estimating the Relative Excess Risk Due to Interaction: A Bayesian Approach

Chu, Haitaoa; Nie, Leib; Cole, Stephen R.c

doi: 10.1097/EDE.0b013e318208750e
Methods: Original Article

The relative excess odds or risk due to interaction (ie, RERIOR and RERI) play an important role in epidemiologic data analysis and interpretation. Previous authors have advocated frequentist approaches based on nonparametric bootstrap, the method of variance estimates recovery, and profile likelihood for estimating confidence intervals. As an alternative, we propose a Bayesian approach that accounts for parameter constraints and estimates the RERIOR in a case-control study from a linear additive odds-ratio model, or the RERI in a cohort study from a linear additive risk-ratio model. We show that Bayesian credible intervals can often be obtained more easily than frequentist confidence intervals. Furthermore, the Bayesian approach can be easily extended to adjust for confounders. Because posterior computation with inequality constraints can be accomplished easily using free software, the proposed Bayesian approaches may be useful in practice.

From the aDivision of Biostatistics, The University of Minnesota, Minneapolis, MN; bDivision of Biometrics IV, Office of Biometrics/CDER/OTS/FDA, Spring, MD; and cDepartment of Epidemiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC.

Submitted 19 May 2010; accepted 18 October 2010; posted 12 January 2011.

Disclaimer for Lei Nie: Views expressed are the author's professional opinions and do not necessarily represent the official positions of the US Food and Drug Administration.

Correspondence: Haitao Chu, Division of Biostatistics, School of Public Health, A460 Mayo Building, MMC 303, The University of Minnesota, Minneapolis, MN 55455. E-mail:

© 2011 Lippincott Williams & Wilkins, Inc.