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，并开发参数模型构建工具。将执行计算机模拟研究，以验证渐近理论开发是有用的干扰样本量通常遇到的生物医学数据集在本提案中描述。在建议的资助期内，我们会研究以下问题：1.非参数回归的加性模型中的估计：本文提出了一种在多元回归中拟合加性模型的算法。估计量的一致性应保持不变，而不限制协变量之间的依赖性。2.多变量纵向数据的非参数回归分析a.本研究项目的动机是从I期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。在进入研究时监测几种激素的水平，并在此后重复监测。这是Staniswalis和Lee（1997）报告的研究的延续。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的发展，以表征四种不同激素随时间的变化之间的关联，并确定是否依赖于屈洛昔芬的剂量。B.当有兴趣用从另一组变量构造的预测器来预测一组变量时，使用冗余分析。为了这个特定的目标，这个标准的多变量方法的冗余分析向量将被扩展到了解如何收集的随机曲线可以被用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.