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      Estimating measures of interaction on an additive scale for preventive exposures


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          Measures of interaction on an additive scale (relative excess risk due to interaction [RERI], attributable proportion [AP], synergy index [S]), were developed for risk factors rather than preventive factors. It has been suggested that preventive factors should be recoded to risk factors before calculating these measures. We aimed to show that these measures are problematic with preventive factors prior to recoding, and to clarify the recoding method to be used to circumvent these problems. Recoding of preventive factors should be done such that the stratum with the lowest risk becomes the reference category when both factors are considered jointly (rather than one at a time). We used data from a case-control study on the interaction between ACE inhibitors and the ACE gene on incident diabetes. Use of ACE inhibitors was a preventive factor and DD ACE genotype was a risk factor. Before recoding, the RERI, AP and S showed inconsistent results (RERI = 0.26 [95%CI: −0.30; 0.82], AP = 0.30 [95%CI: −0.28; 0.88], S = 0.35 [95%CI: 0.02; 7.38]), with the first two measures suggesting positive interaction and the third negative interaction. After recoding the use of ACE inhibitors, they showed consistent results (RERI = −0.37 [95%CI: −1.23; 0.49], AP = −0.29 [95%CI: −0.98; 0.40], S = 0.43 [95%CI: 0.07; 2.60]), all indicating negative interaction. Preventive factors should not be used to calculate measures of interaction on an additive scale without recoding.

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          Most cited references10

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          On the estimation of additive interaction by use of the four-by-two table and beyond.

          G Zou (2008)
          A four-by-two table with its four rows representing the presence and absence of gene and environmental factors has been suggested as the fundamental unit in the assessment of gene-environment interaction. For such a table to be more meaningful from a public health perspective, it is important to estimate additive interaction. A confidence interval procedure proposed by Hosmer and Lemeshow has become widespread. This article first reveals that the Hosmer-Lemeshow procedure makes an assumption that confidence intervals for risk ratios are symmetric and then presents an alternative that uses the conventional asymmetric intervals for risk ratios to set confidence limits for measures of additive interaction. For the four-by-two table, the calculation involved requires no statistical programs but only elementary calculations. Simulation results demonstrate that this new approach can perform almost as well as the bootstrap. Corresponding calculations in more complicated situations can be simplified by use of routine output from multiple regression programs. The approach is illustrated with three examples. A Microsoft Excel spreadsheet and SAS codes for the calculations are available from the author and the Journal's website, respectively.
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            The estimation of synergy or antagonism.

            K Rothman (1976)
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              Estimation of the relative excess risk due to interaction and associated confidence bounds.

              The relative excess risk due to interaction (RERI) provides a useful metric of departure from additivity of effects on a relative risk scale. In this paper, the authors show that RERI is identical to the product term in a linear odds ratio or a linear relative risk model. SAS and STATA codes are provided for fitting a linear odds ratio model that directly parameterizes RERI. In addition, this paper presents a method for obtaining likelihood-based 95% confidence bound estimates for RERI. The authors show that likelihood-based confidence intervals may differ substantially from the asymptotic confidence interval estimates advocated by previous authors. The approach presented in this paper should facilitate estimation of RERI and associated likelihood-based confidence bounds, by using standard statistical packages.

                Author and article information

                +0031-88-7551168 , +0031-88-7568099 , m.j.knol@umcutrecht.nl
                Eur J Epidemiol
                European Journal of Epidemiology
                Springer Netherlands (Dordrecht )
                23 February 2011
                23 February 2011
                June 2011
                : 26
                : 6
                : 433-438
                [1 ]Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, PO Box 85500, 3508 GA Utrecht, The Netherlands
                [2 ]Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA USA
                [3 ]Division of Pharmacoepidemiology and Pharmacotherapy, Utrecht Institute for Pharmaceutical Sciences, Utrecht University, Utrecht, The Netherlands
                © The Author(s) 2011
                Custom metadata
                © Springer Science+Business Media B.V. 2011

                Public health
                interaction,preventive factors,synergy index,relative excess risk due to interaction


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