Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes

Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes
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有或没有零峰值的双变量协变量的剂量响应模型:二元结果的理论和应用

DOI:
10.1111/stan.12064
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发表时间:
2015
影响因子:
1.5
通讯作者:
Becher H
Becher H
中科院分区:
数学4区
文献类型:
--
作者:
Lorenz E;Jenkner C;Sauerbrei W;Becher H

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在流行病学和临床研究中,经常有一部分未暴露的个体导致暴露值为零,这意味着一些个体没有暴露,而暴露的个体具有某种连续分布。例如吸烟或饮酒。我们将这些变量称为峰值为零的变量 (SAZ)。在本文中,我们对如何使用 SAZ 进行协变量建模进行了系统研究,并为选定的双变量分布导出了理论优势比函数。我们考虑具有 SAZ 的二元正态分布和二元对数正态分布。混杂和效应修改都可以通过给定二元结果变量 Y 形式化协方差矩阵来优雅地描述。为了对这些变量的影响进行建模,我们使用了基于分数多项式的程序,该程序首先由 Royston 和 Altman (1994,Applied Statistics43: 429–467) 引入,并针对 SAZ 情况进行了修改(Royston 和 Sauerbrei, 2008,多变量模型构建:基于分数多项式用于连续变量建模的实用回归分析方法,Wiley;Becheret 等人, 2012,生物识别杂志54:686–700)。我们的目标是为流行病学和临床研究中的理论、实践程序和应用做出贡献,以导出具有 SAZ 的变量的多变量模型。例如,我们使用肺癌病例对照研究的数据。
In epidemiology and clinical research, there is often a proportion of unexposed individuals resulting in zero values of exposure, meaning that some individuals are not exposed and those exposed have some continuous distribution. Examples are smoking or alcohol consumption. We will call these variables with a spike at zero (SAZ). In this paper, we performed a systematic investigation on how to model covariates with a SAZ and derived theoretical odds ratio functions for selected bivariate distributions. We consider the bivariate normal and bivariate log normal distribution with a SAZ. Both confounding and effect modification can be elegantly described by formalizing the covariance matrix given the binary outcome variableY. To model the effect of these variables, we use a procedure based on fractional polynomials first introduced by Royston and Altman (1994,Applied Statistics43: 429–467) and modified for the SAZ situation (Royston and Sauerbrei, 2008,Multivariable model‐building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables, Wiley; Becheret al., 2012,Biometrical Journal54: 686–700). We aim to contribute to theory, practical procedures and application in epidemiology and clinical research to derive multivariable models for variables with a SAZ. As an example, we use data from a case–control study on lung cancer.
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