SEMIPARAMETRIC REGRESSION TECHNIQUES FOR THE ANALYSIS OF BIOMEDICAL DATA

该研究计划的长期目标是开发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，并开发用于参数建模的工具。将执行计算机模拟研究，以验证所开发的渐近理论对于干扰在本提案中描述的生物医学数据集中通常遇到的样本大小是有用的。1.非参数回归的加性模型中的估计：提出了一种多元回归中加性模型的拟合算法。估计量的一致性应该保持，而不限制协变量之间的相关性。2.多元纵向数据的非参数回归分析。A.这项研究项目的动机是从第一阶段研究中获得的数据集，以确定屈洛昔芬在晚期转移性乳腺癌患者中的安全性。在进入这项研究时，对几种激素的水平进行了监测，此后反复进行监测。这是Staniswalis和Lee(1997)报告的研究的继续。协方差函数的光滑非参数估计将被进一步研究。提出了随机曲线的典型相关分析方法，以表征四种不同激素随时间的相关性，并确定是否存在对屈洛昔芬剂量的依赖。B.当需要用由另一组变量构造的预测器来预测一组变量时，可以使用冗余分析。为了达到这个特定的目的，这个标准的多变量向量冗余分析方法将被扩展，以理解如何使用一组随机曲线来最好地预测另一组随机曲线。

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.