Using Generalized Additive Models to Detect and Estimate Threshold Associations

IF 1.2 4区 数学
A. Benedetti, M. Abrahamowicz, K. Leffondré, M. Goldberg, R. Tamblyn
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引用次数: 16

Abstract

In a variety of research settings, investigators may wish to detect and estimate a threshold in the association between continuous variables. A threshold model implies a non-linear relationship, with the slope changing at an unknown location. Generalized additive models (GAMs) (Hastie and Tibshirani, 1990) estimate the shape of the non-linear relationship directly from the data and, thus, may be useful in this endeavour.We propose a method based on GAMs to detect and estimate thresholds in the association between a continuous covariate and a continuous dependent variable. Using simulations, we compare it with the maximum likelihood estimation procedure proposed by Hudson (1966).We search for potential thresholds in a neighbourhood of points whose mean numerical second derivative (a measure of local curvature) of the estimated GAM curve was more than one standard deviation away from 0 across the entire range of the predictor values. A threshold association is declared if an F-test indicates that the threshold model fit significantly better than the linear model.For each method, type I error for testing the existence of a threshold against the null hypothesis of a linear association was estimated. We also investigated the impact of the position of the true threshold on power, and precision and bias of the estimated threshold.Finally, we illustrate the methods by considering whether a threshold exists in the association between systolic blood pressure (SBP) and body mass index (BMI) in two data sets.
利用广义加性模型检测和估计阈值关联
在各种研究设置中,研究者可能希望检测和估计连续变量之间关联的阈值。阈值模型意味着一种非线性关系,斜率在未知位置变化。广义加性模型(GAMs) (Hastie和Tibshirani, 1990)直接从数据中估计非线性关系的形状,因此,在这一努力中可能有用。我们提出了一种基于GAMs的方法来检测和估计连续协变量和连续因变量之间关联的阈值。通过模拟,我们将其与Hudson(1966)提出的最大似然估计过程进行了比较。我们在估计的GAM曲线的平均数值二阶导数(局部曲率的度量)在整个预测值范围内距离0超过一个标准差的点的邻域中搜索潜在阈值。如果f检验表明阈值模型明显优于线性模型,则声明阈值关联。对于每种方法,对线性关联的零假设检验阈值存在性的类型I误差进行了估计。我们还研究了真实阈值的位置对功率的影响,以及估计阈值的精度和偏差。最后,我们通过考虑收缩压(SBP)和体重指数(BMI)之间的关联是否存在阈值来说明方法。
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来源期刊
International Journal of Biostatistics
International Journal of Biostatistics Mathematics-Statistics and Probability
CiteScore
2.30
自引率
8.30%
发文量
28
期刊介绍: The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.
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