Adaptive Methodology for Functional Biomedical Data

描述(申请人提供)：越来越多的生物医学研究产生功能数据，其中理想的观察单位是曲线。这个研究项目的目标是开发新的贝叶斯方法，为曲线样本的非参数估计和推断提供一个统一的框架。这些方法将足够灵活地对从各种实验设计获得的函数进行建模，为广泛的研究问题提供答案，并将足够的适应性应用于来自广泛应用的函数数据。我们将应用这些方法来模拟来自一系列与癌症相关的生物医学研究的功能数据，这些研究激励了我们的方法论思维。我们提出的方法适用于具有大量局部特征(如峰值)的函数数据，因为我们采用了自适应正则化过程，在最小程度地衰减主导局部特征的情况下对函数进行去噪。这项研究的具体目的是： 1.提出了一种用于曲线样本建模的统一函数混合模型框架。发展了一种基于小波的方法来拟合该模型，并获得了固定和随机效应函数以及协方差参数的自适应正则化非参数估计和贝叶斯推断。 2.提出了在功能混合模型中进行形式化贝叶斯推理和模型选择的方法。这种方法的应用包括检验固定/随机效应的函数假设，比较具有不同协方差结构的模型，确定基函数，检验不同功能响应之间的相关性，以及确定合适的分段常量间隔模型。 3.发展了小波正则化函数主成分分析方法。将我们在特定目标1和2中发展的基于小波的函数混合模型方法扩展到其他基函数，包括小波正则化的特征函数和样条线。 4.将我们在特定目标1、2和3中开发的方法应用于一系列涉及功能数据的生物医学应用，包括结肠癌发生研究、星球健康儿童活动研究、调查急性肾功能衰竭的动物研究以及涉及蛋白质组学的医学研究。 5.制作公开可用的统计软件，以实施本提案中提出的方法。

DESCRIPTION (provided by applicant): An ever-increasing number of biomedical studies yield functional data, in which the ideal units of observation are curves. The goal of this research program is to develop new Bayesian methodology that provides a unifying framework for performing nonparametric estimation and inference for samples of curves. These methods will be flexible enough to model functions obtained from a variety of experimental designs, provide answers to a broad range of research questions, and will be sufficiently adaptive to apply to functional data from a wide range of applications. We will apply these methods to model functional data from a series of cancer-related biomedical studies that have motivated our methodological thinking. The methods we propose are appropriate for functional data characterized by numerous local features like peaks since we employ adaptive regularization procedures which denoise the functions with minimal attenuation of the dominant local features. The specific aims of this research are: 1. Introduce a unified functional mixed model framework for modeling samples of curves. Develop a wavelet-based method to fit this model and obtain adaptively regularized nonparametric estimates and Bayesian inference for fixed and random effect functions as well as covariance parameters. 2. Develop methodology to perform formal Bayesian inference and model selection in functional mixed models. Applications of this method include testing functional hypotheses on fixed/random effects, comparing models with different covariance structures, determining the number of basis functions, testing for correlation among different functional responses, and identifying appropriate piecewise constant compartment models. 3. Develop methods to perform wavelet-regularized functional principal component analysis. Extend our wavelet-based functional mixed model methods developed in Specific Aims 1 and 2 to other basis functions, including wavelet-regularized eigen functions and splines. 4. Apply the methods we develop in Specific Aims 1, 2, and 3 to a series of biomedical applications involving functional data, including colon carcinogenesis studies, a Planet Health children's activity study, an animal study investigating acute renal failure, and medical studies involving proteomics. 5. Produce publicly available statistical software for implementing the methods developed in this proposal.