Becher Heiko, Lorenz Eva, Royston Patrick, Sauerbrei Willi
Institute of Public Health, Medical Faculty, University of Heidelberg, Im Neuenheimer Feld 324, 69120 Heidelberg, Germany.
Biom J. 2012 Sep;54(5):686-700. doi: 10.1002/bimj.201100263. Epub 2012 Jul 9.
In epidemiology and in clinical research, risk factors often have special distributions. A common situation is that a proportion of individuals have exposure zero, and among those exposed, we have some continuous distribution. We call this a 'spike at zero'. Examples for this are smoking, duration of breastfeeding, or alcohol consumption. Furthermore, the empirical distribution of laboratory values and other measurements may have a semi-continuous distribution as a result of the lower detection limit of the measurement. To model the dose-response function, an extension of the fractional polynomial approach was recently proposed. In this paper, we suggest a modification of the previously suggested FP procedure. We first give the theoretical justification of this modified procedure by investigating relevant distribution classes. Here, we systematically derive the theoretical shapes of dose-response curves under given distributional assumptions (normal, log normal, gamma) in the framework of a logistic regression model. Further, we check the performance of the procedure in a simulation study and compare it to the previously suggested method, and finally we illustrate the procedures with data from a case-control study on breast cancer.
在流行病学和临床研究中，风险因素往往具有特殊的分布。一种常见的情况是，一部分个体的暴露量为零，而在那些暴露的个体中，我们有某种连续分布。我们将此称为“零处的尖峰”。吸烟、母乳喂养持续时间或饮酒就是这种情况的例子。此外，由于测量的检测下限，实验室值和其他测量的经验分布可能具有半连续分布。为了对剂量反应函数进行建模，最近有人提出了分数多项式方法的扩展。在本文中，我们建议对先前提出的FP程序进行修改。我们首先通过研究相关分布类别来给出这种修改后程序的理论依据。在此，我们在逻辑回归模型的框架内，系统地推导了在给定分布假设（正态、对数正态、伽马）下剂量反应曲线的理论形状。此外，我们在模拟研究中检验该程序的性能，并将其与先前提出的方法进行比较，最后我们用一项乳腺癌病例对照研究的数据来说明这些程序。
