Knol Mirjam J, van der Tweel Ingeborg, Grobbee Diederick E, Numans Mattijs E, Geerlings Mirjam I
Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, The Netherlands.
Int J Epidemiol. 2007 Oct;36(5):1111-8. doi: 10.1093/ije/dym157. Epub 2007 Aug 27.
To determine the presence of interaction in epidemiologic research, typically a product term is added to the regression model. In linear regression, the regression coefficient of the product term reflects interaction as departure from additivity. However, in logistic regression it refers to interaction as departure from multiplicativity. Rothman has argued that interaction estimated as departure from additivity better reflects biologic interaction. So far, literature on estimating interaction on an additive scale using logistic regression only focused on dichotomous determinants. The objective of the present study was to provide the methods to estimate interaction between continuous determinants and to illustrate these methods with a clinical example.
and results From the existing literature we derived the formulas to quantify interaction as departure from additivity between one continuous and one dichotomous determinant and between two continuous determinants using logistic regression. Bootstrapping was used to calculate the corresponding confidence intervals. To illustrate the theory with an empirical example, data from the Utrecht Health Project were used, with age and body mass index as risk factors for elevated diastolic blood pressure.
The methods and formulas presented in this article are intended to assist epidemiologists to calculate interaction on an additive scale between two variables on a certain outcome. The proposed methods are included in a spreadsheet which is freely available at: http://www.juliuscenter.nl/additive-interaction.xls.
为了在流行病学研究中确定交互作用的存在，通常会在回归模型中添加一个乘积项。在线性回归中，乘积项的回归系数反映的交互作用是相对于可加性的偏离。然而，在逻辑回归中，它指的交互作用是相对于可乘性的偏离。罗斯曼认为，以相对于可加性的偏离来估计的交互作用能更好地反映生物学交互作用。到目前为止，关于使用逻辑回归在可加尺度上估计交互作用的文献仅关注二分决定因素。本研究的目的是提供估计连续决定因素之间交互作用的方法，并通过一个临床实例来说明这些方法。
我们从现有文献中推导了使用逻辑回归来量化一个连续决定因素与一个二分决定因素之间以及两个连续决定因素之间相对于可加性的偏离的交互作用的公式。采用自助法计算相应的置信区间。为了用一个实证例子说明该理论，我们使用了乌得勒支健康项目的数据，将年龄和体重指数作为舒张血压升高的危险因素。
本文提出的方法和公式旨在帮助流行病学家计算两个变量在某一结局上的可加尺度上的交互作用。所提出的方法包含在一个电子表格中，可从以下网址免费获取：http://www.juliuscenter.nl/additive - interaction.xls。
