Parexel, Waltham, Massachusetts, USA.
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA.
Biometrics. 2023 Dec;79(4):3388-3401. doi: 10.1111/biom.13900. Epub 2023 Jul 17.
Varying coefficient models have been used to explore dynamic effects in many scientific areas, such as in medicine, finance, and epidemiology. As most existing models ignore the existence of zero regions, we propose a new soft-thresholded varying coefficient model, where the coefficient functions are piecewise smooth with zero regions. Our new modeling approach enables us to perform variable selection, detect the zero regions of selected variables, obtain point estimates of the varying coefficients with zero regions, and construct a new type of sparse confidence intervals that accommodate zero regions. We prove the asymptotic properties of the estimator, based on which we draw statistical inference. Our simulation study reveals that the proposed sparse confidence intervals achieve the desired coverage probability. We apply the proposed method to analyze a large-scale preoperative opioid study.
变系数模型已被广泛应用于医学、金融和流行病学等多个科学领域，以探索其中的动态效应。由于现有大多数模型都忽略了零区域的存在，我们提出了一种新的软阈值变系数模型，其中系数函数具有分段平滑的零区域。我们的新建模方法能够进行变量选择、检测选定变量的零区域、获得具有零区域的变系数的点估计，并构建一种新的稀疏置信区间类型，以适应零区域。我们基于该估计器的渐近性质证明了统计推断。我们的模拟研究表明，所提出的稀疏置信区间能够达到期望的覆盖概率。我们将所提出的方法应用于一项大型术前阿片类药物研究的分析。
