SEMIPARAMETRIC REGRESSION TECHNIQUES FOR THE ANALYSIS OF BIOMEDICAL DATA

研究目标的总体主旨是在以下方面取得进展 为各种应用和实验设计提供 常用参数回归方法的半参数替代 用于数据分析。提出了离散型和离散型的方法学 连续的数据以及独立和相关的答复。这个 研究的目标是：i)回归的非参数估计 函数，当解释变量是离散的时，ii)估计 剂量效应在剂量-反应实验中给出随时间的观察结果，以及 剂量与时间相互作用的非参数检测，III) 有条件指定分布中的估计。 基于错误的数据分析的决策和建议 参数模型是不可靠的。这就是对 半参数模型与数据拟合方法的发展。这个 本提案中概述的基础研究工作包括：一)理论 工作，ii)计算机模拟以验证程序，以及iii) 半参数方法在生物医学数据处理中的应用 弗吉尼亚联邦大学医学院的研究人员 弗吉尼亚州，德克萨斯大学安德森癌症中心和眼睛 威斯康星大学麦迪逊分校。这个项目还 包括本科生辅导和社区外展 组件。数学系本科生 科学部将协助研究项目和数学。 为埃尔帕索地区中学生设计的外展活动。

The overall thrust of the research objectives is to make progress towards providing, for a wide variety of applications and experimental designs, a semi-parametric alternative to the popular parametric regression methods used in the analysis of data. Methodology is proposed for discrete and continuous data as well as for independent and correlated responses. The objectives are to study; i) nonparametric estimation of a regression function when the explanatory variable is discrete, ii) estimation of the dose effect given observations over time in a dose-response experiment, and nonparametric detection of interactions between dose and time, iii) estimation in conditionally specified distributions. Decisions and recommendations based on data analysis using the wrong parametric model are not reliable. Therein lies the need for the development of methodology for fitting semiparametric models to data. The basic research efforts outlined in this proposal include: I) theoretical work, ii) computer simulations to validate the procedures, and iii) application of the semiparametric methods to biomedical data obtained from researchers at Virginia Commonwealth University - Medical College of Virginia, The University of Texas M.D. Anderson Cancer Center, and The Eye Institute of the University of Wisconsin, Madison. This project also includes an undergraduate student mentorship and community outreach component. Undergraduate students in the Department of Mathematical Sciences will assist with the research projects and with mathematics outreach activities designed for the El Paso area Middle School students.