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首页> 外文期刊>Statistics in medicine >Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data.
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Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data.

机译：功能性线性回归模型中的假设检验，采用Neyman截断和小波阈值处理纵向数据。

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摘要

Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.
机译：生物医学研究中的纵向数据集通常包含大量重复测量。在许多情况下，轨迹看起来不像是全局线性或多项式，因此很难使用基于各种线性模型的标准纵向数据分析来汇总数据或检验假设。一种替代方法是应用功能数据分析的方法，该方法直接针对离散采样的重复测量基础下的连续非线性曲线。出于数据探索的目的，已经基于各种平滑方案开发了许多功能数据分析策略，但是用于进行关于预测结果关系的因果推断的选项较少，这是假设驱动医学研究中常见的任务。为了比较曲线组，已提出了两种具有良好功效的测试策略，用于高维方差分析：基于傅立叶的自适应Neyman检验和基于小波的阈值检验。使用戒烟临床试验数据集，本文演示了如何将假设检验的策略扩展到具有连续功能响应和分类或连续标量预测变量的功能线性回归模型（FLRM）的框架中。分析过程包括三个步骤：首先，对原始的重复测量应用傅里叶变换或小波变换;然后在转换后的域中拟合多元线性模型;最后，使用自适应Neyman或阈值统计量测试回归系数。由于FLRM可以看作是传统的多元线性回归模型的自然扩展，因此该模型和计算工具的开发应增强纵向数据的医学统计能力。

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