NEW FUNCTIONAL MODELS FOR BIOMEDICAL DATA

描述（改编自申请人的摘要）：函数数据是常见的 在癌症研究和其他生物医学研究中， 随着时间的推移，在癌症实验和其他临床试验中，生长曲线， 激素谱、生物信号的昼夜节律和药物活性。 尽管在独立数据的函数模型方面已经做了很多工作， 将复杂的设计和相关性结合起来的扩展仍然非常 初步的本申请的第一个具体目标是开发通用的 使用平滑样条函数的功能模型，可以包含复杂的设计 并允许灵活的非参数曲线间随机效应。另一 函数模型长期存在的问题是计算量大。 除了在非常简单的情况下，目前的大多数估计程序需要 求高维矩阵的逆这将阻止应用程序对大数据 集.在这个应用程序中，我们将开发O（N）序贯估计 一般函数模型的卡尔曼修正程序 滤波和固定间隔平滑。 连续测量已经成为患者监测的自然部分， 医学诊断在监测和预测患者特定的结果 基于实验室测试或其他生物标志物，我们可以获得更准确的 通过借用现有患者群体的力量进行预测 随着时间的推移。在医疗诊断中，我们可以通过使用 最新的累积信息，并将个人资料与 现有的组配置文件。在这个应用程序中，我们将开发动态患者 监测和诊断方法，其中灵活的功能模型将 用于对总体和个体概况进行建模。与拟议 序贯估计程序，这些方法可以有效地计算 并在真实的时间设置中实施，这导致快速医疗 干预措施。 目前大多数统计推断程序依赖于分布 假设，如常态假设。当分布为 多模态，通常很难进行参数假设，因此 需要非参数密度估计方法。在本申请中，我们 将开发一般密度模型及其相关的推理程序， 并将这些方法应用于可访问的生物医学数据集。

DESCRIPTION (Adapted from the Applicant's Abstract): Functional data are common in cancer studies and other biomedical research, such as biomarkers measured over time in cancer experiments and other clinical trials, growth curves, hormone profiles, circadian rhythms in biological signals and drug activities. Although much work has been done on functional models for independent data, extensions to incorporate complex designs and correlations are still very preliminary. The first specific aim of this application is to develop general functional models using smoothing splines that can incorporate complex designs and allow flexible nonparametric between-curve random effects. Another long-existing problem for functional models is the heavy computational demand. Except in very simple cases, most of the current estimation procedures need to invert large dimensional matrices. This prevents applications to large data sets. In this application, we will develop O(N) sequential estimation procedures for general functional models by modifications of the Kalman filtering and fixed interval smoothing. Serial measurements have become a natural part of patient monitoring and medical diagnosis. In monitoring and predicting a patient-specific outcome based on laboratory tests or other biomarkers, we can obtain more accurate predictions by borrowing the strength from the existing patient population profiles over time. In medical diagnosis, we can gain efficiency by using the up-to-date cumulative information and compare the individual profile with the existing group profiles. In this application, we will develop dynamic patient monitoring and diagnostic methods, in which flexible functional models will be used to model both the population and individual profiles. With the proposed sequential estimation procedures, these methods can be efficiently calculated and implemented in a real time setting, which leads to rapid medical interventions. Most current statistical inference procedures rely on the distributional assumptions, such as the normality assumption. When the distribution is multimodal, it is often difficult to make parametric assumptions, and therefore nonparametric density estimation methods are needed. In this application, we will develop general density models and their associated inference procedures, and apply these methods to accessible biomedical data sets.