American Journal of Epidemiology Advance Access published online on May 28, 2008
American Journal of Epidemiology, doi:10.1093/aje/kwn104
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Original Contribution |
On the Estimation of Additive Interaction by Use of the Four-by-two Table and Beyond
1 Department of Epidemiology and Biostatistics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, Ontario, Canada
2 Robarts Clinical Trials, Robarts Research Institute, Schulich School of Medicine and Dentistry, University of Western Ontario, London, Ontario, Canada
Correspondence to Dr. G. Y. Zou, Department of Epidemiology and Biostatistics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, Ontario, Canada N6A 5C1 (e-mail: gzou{at}robarts.ca).
Received for publication September 14, 2007. Accepted for publication March 27, 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.
bootstrap; genotype-environment interaction; logistic regression; proportional hazards models; risk ratio
Abbreviations: AP, attributable proportion due to interaction; CI, confidence interval; OR, odds ratio; RERI, relative excess risk due to interaction; RR, risk ratio; SA, simple asymptotic; SI, synergy index
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