SEMIPARAMETRIC REGRESSION TECHNIQUES FOR THE ANALYSIS OF BIOMEDICAL DATA

本研究计划的长期目标是发展基于非参数和半参数曲线估计理论的分析和生物医学数据的统计方法，并开发参数模型构建工具。将进行计算机模拟研究，以验证所开发的渐近理论对本提案中描述的生物医学数据集中通常遇到的样本量干扰是有用的。在拟议的资助期内将研究下列问题：非参数回归中加性模型的估计：本文提出了一种多元回归中加性模型的拟合算法。估计量的一致性不应限制协变量之间的相关性。2. 多变量纵向数据的非参数回归分析。a.本研究项目的动机来自于确定德洛昔芬在晚期转移性乳腺癌患者中的安全性的I期研究数据集。在研究开始时监测几种激素的水平，并在之后反复监测。这是Staniswalis和Lee（1997）报告的研究的延续。本文将进一步研究协方差函数的光滑非参数估计。研究人员提出了一种随机曲线典型相关分析方法，以表征四种不同激素之间随时间的相关性，并确定是否与德洛昔芬的剂量有关。b.当有兴趣用由另一组变量构建的预测器来预测一组变量时，使用冗余分析。为了这个特定的目的，这个标准的多变量向量冗余分析方法将被扩展，以理解如何使用随机曲线的集合来最好地预测另一个随机曲线的集合。

The long term goals of this research program are to develop statistical methodology for the analysis and biomedical data that is based on non- and semi-parametric curve estimation theory, and to develop tools for parametric model building. Computer simulation studies will be executed to verify that the asymptotic theory developed is useful for interference with sample sizes typically encountered in biomedical data sets described in this proposal. The following problems will be studied during the proposed funding period: 1. Estimation in the Additive Model for Non-parametric Regression: An algorithm is proposed here for fitting the additive model in multiple regression. Consistency of the estimators should hold without restricting dependencies among the co-variates. 2. Non-parametric Regression Analysis of Multi-variate Longitudinal Data. a. This research project is motivated by a data set that was obtained from Phase I study to determine the safety of Droloxifene in patients with advanced metastatic breast cancer. The levels of several hormones were monitored at the time of entry to the study and repeatedly thereafter. This is a continuation of research reported in Staniswalis and Lee (1997). The smooth non-parametric estimators of the covariance function will be studied further. Development of methods for a canonical correlation analysis for random curves is proposed to characterize associations among the four different hormones over time, and to determine if there is a dependence on the dose of Droloxifene. b. Redundancy analysis is used when it is of interest to predict one set of variables with a predictor constructed from another set of variables. For this specific aim, this standard multi-variate methodology of redundancy analysis for vectors will be extended to understand how a collection of random curves could be used to best predict another collection of random curves.