Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, New York, NY 10065, USA.
Stat Med. 2013 Mar 30;32(7):1164-90. doi: 10.1002/sim.5628. Epub 2012 Sep 27.
This paper is concerned with evaluating whether an interaction between two sets of risk factors for a binary trait is removable and, when it is removable, fitting a parsimonious additive model using a suitable link function to estimate the disease odds (on the natural logarithm scale). Statisticians define the term 'interaction' as a departure from additivity in a linear model on a specific scale on which the data are measured. Certain interactions may be eliminated via a transformation of the outcome such that the relationship between the risk factors and the outcome is additive on the transformed scale. Such interactions are known as removable interactions. We develop a novel test statistic for detecting the presence of a removable interaction in case-control studies. We consider the Guerrero and Johnson family of transformations and show that this family constitutes an appropriate link function for fitting an additive model when an interaction is removable. We use simulation studies to examine the type I error and power of the proposed test and to show that, when an interaction is removable, an additive model based on the Guerrero and Johnson link function leads to more precise estimates of the disease odds parameters and a better fit. We illustrate the proposed test and use of the transformation by using case-control data from three published studies. Finally, we indicate how one can check that, after transformation, no further interaction is significant.
本文旨在评估二项分类性状的两组风险因素之间的交互作用是否可以消除，以及当交互作用可以消除时，使用合适的链接函数拟合简约的加性模型，以估计疾病的优势比（自然对数尺度）。统计学家将“交互作用”一词定义为在线性模型中偏离特定尺度上的可加性，而数据是在该尺度上测量的。通过对结果进行转换，可以消除某些交互作用，从而使风险因素与结果之间的关系在转换后的尺度上具有加性。这种交互作用被称为可消除的交互作用。我们开发了一种新的检验统计量，用于检测病例对照研究中可消除交互作用的存在。我们考虑了 Guerrero 和 Johnson 变换族，并表明当交互作用可以消除时，该变换族构成了拟合加性模型的合适链接函数。我们使用模拟研究来评估拟议检验的Ⅰ型错误和功效，并表明当交互作用可以消除时，基于 Guerrero 和 Johnson 链接函数的加性模型可以更准确地估计疾病优势比参数，并具有更好的拟合度。我们通过使用来自三个已发表研究的病例对照数据来说明拟议的检验和变换的使用。最后，我们指出如何检查转换后是否没有其他交互作用具有统计学意义。
