Modeling continuous covariates with a “spike” at zero: Bivariate approaches
Modeling continuous covariates with a “spike” at zero: Bivariate approaches
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对“尖峰”为零的连续协变量进行建模：双变量方法
DOI：
10.1002/bimj.201400112
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发表时间：
2016
影响因子：
1.7
通讯作者：
Sauerbrei W
中科院分区：
文献类型：
--
作者：
Jenkner C;Lorenz E;Becher H;Sauerbrei W
在流行病学和临床研究中，预测因子通常对大量观测值取零值，而其余观测值的分布是连续的。这些预测变量被称为峰值为零的变量。例如吸烟或饮酒。最近，一个扩展的分数多项式（FP）的过程，一种技术建模的非线性关系，提出了处理这种情况。为了指示值是否为零，将二进制变量添加到模型中。在称为FP-spike的两阶段程序中，评估二元变量和/或连续FP函数对于正部分的必要性，以获得合适的拟合。在单变量分析中，FP-spike程序通常会导致易于解释的函数关系。本文介绍了四种处理两个变量在零点有尖峰的方法。这些方法依赖于零值和非零值的二元分布。Bi-Sep是四种双变量方法中最简单的一种。它对两个SAZ变量分别使用单变量FP-spike程序。在Bi‐D3、Bi‐D1和Bi‐Sub中，在二进制指标中同时考虑两个变量中零的比例。因此，这些策略可以解释相关变量。该方法可用于任意分布的协变量。为了说明和比较结果，考虑了来自喉癌病例对照研究的数据，吸烟和饮酒作为两个SAZ变量。此外，一个可能的扩展到三个或更多的SAZ变量概述。提出了结合双变量方法进行相关性分析的对数线性模型组合。
In epidemiology and clinical research, predictors often take value zero for a large amount of observations while the distribution of the remaining observations is continuous. These predictors are called variables with a spike at zero. Examples include smoking or alcohol consumption. Recently, an extension of the fractional polynomial (FP) procedure, a technique for modeling nonlinear relationships, was proposed to deal with such situations. To indicate whether or not a value is zero, a binary variable is added to the model. In a two stage procedure, called FP‐spike, the necessity of the binary variable and/or the continuous FP function for the positive part are assessed for a suitable fit. In univariate analyses, the FP‐spike procedure usually leads to functional relationships that are easy to interpret. This paper introduces four approaches for dealing with two variables with a spike at zero (SAZ). The methods depend on the bivariate distribution of zero and nonzero values. Bi‐Sep is the simplest of the four bivariate approaches. It uses the univariate FP‐spike procedure separately for the two SAZ variables. In Bi‐D3, Bi‐D1, and Bi‐Sub, proportions of zeros in both variables are considered simultaneously in the binary indicators. Therefore, these strategies can account for correlated variables. The methods can be used for arbitrary distributions of the covariates. For illustration and comparison of results, data from a case‐control study on laryngeal cancer, with smoking and alcohol intake as two SAZ variables, is considered. In addition, a possible extension to three or more SAZ variables is outlined. A combination of log‐linear models for the analysis of the correlation in combination with the bivariate approaches is proposed.
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