On the Estimation of Additive Interaction by Use of the Four-by-two Table and Beyond

Abstract

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.

Relationships Between Fine Particulate Air Pollution, Cardiometabolic Disorders, and Cardiovascular Mortality

“…To test for additive interactions between PM 2.5 exposure and key cardiometabolic risk factors formally, the relative excess risk because of interaction, the attributable proportion because of interaction and the synergy index were calculated using the MOVER method for the analysis of 4×2 tables as documented elsewhere. 24 The second approach to evaluate the effect modification of cardiometabolic risk factors estimated adjusted HRs associated with increases in PM 2.5 (using PM 2.5 as a continuous variable) for cardiovascular mortality, while stratifying by all cardiometabolic risk factors that were available based on information from the ACS CPS-II enrollment questionnaire. These risk factors include body mass index; doctor diagnosed high blood pressure, heart disease, and diabetes mellitus; exercise levels; vegetable/fruit/fiber and fat intake; and the use of medications including aspirin, heart medications, and diuretics.…”

FTO Genotype, Physical Activity, and Coronary Heart Disease Risk in Swedish Men and Women

“…28 We calculated 95% CIs for the 2 RERIs according to formulas by Zou. 29 We also analyzed interaction on the multiplicative (relative risk) scale by introducing the product of FTO genotype (TT=0, TA/ AA=1) and PA level as categorical variable (high, medium, low) in the logistic regression model, using high PA as a reference category. Because there were 3 categories of PA, this yielded 2 interaction terms: FTO×low PA and FTO×medium PA. From this model, we obtained ORs with 95% CIs for each interaction term.…”

Moderation of Adult Depression by a Polymorphism in the FKBP5 Gene and Childhood Physical Abuse in the General Population

“…This method was recommended by Nie et al (2010) to handle low cell counts. This modified approach is based on regularized instead of conventional logistic regression (see Supplementary Materials) and is supposed to yield narrower CIs compared with Zou's (Zou, 2008) formula (Nie et al, 2010). We additionally calculated the more commonly used formula by Zou.…”