Measurement Error, Missing Data and Semiparametrics

描述(由申请人提供)：本建议反映了我们在解决一般回归设置中的测量误差、不完整数据和/或函数(曲线)数据问题方面的持续兴趣。所提出的研究课题来自于各种重要的研究。这些研究包括(I)结肠癌发生项目，该项目由一系列实验组成，以在细胞水平上研究结肠癌的发生；(Ii)人工降解的mRNA粪便微阵列实验，研究人员打算从粪便流中脱落的结肠癌细胞中恢复遗传信息，作为建立非侵入性结肠癌检测工具的第一步；以及(Iii)光谱斜入射反射仪皮肤损伤诊断研究，其目的是使用新开发的生物工程设备来确定反映皮肤损伤病理学的生理特征。我们调查的统计方法可以分为五个主要研究目标：开发和评估具有灵活数据收集设计的一般非参数和半参数回归模型下的边际估计方法。2.发展和评价当一个主要协变量是二次混合模型中的潜在变量时的半参数方法。3.发展和评价有效的半参数方法，以适应不完全数据，使用估计方程和分配-最大化方法。4.发展和评价具有函数协变量和标量响应的相关数据的非参数和半参数广义线性模型方法。5.开发和评估具有较大比例异常观测的微阵列数据的半参数标准化程序。这一建议的主要重点是开发直观、高效和在计算上可行的方法，而不强加不必要的参数假设。我们希望我们在这些有趣的生物学研究上的努力将对癌症研究的进展产生重大影响。

DESCRIPTION (provided by applicant): This proposal reflects our continuing interest in solving problems of measurement error, incomplete data nd/or functional (curve) data in general regression settings. The proposed research topics have arisen aturally from various important studies. These studies include (i) a colon cancer tumorigenesis project, vhich consists of a series of experiments to study .colon cancer tumorigenesis at the cellular level, (ii) artially degraded mRNA fecal microarray experiments, in which the investigators intend to recover genetic nformation from exfoliated colonocytes in the fecal stream as the initial step in building a non-invasive colon .ancer detection tool, and (iii) a spectroscopic oblique incidence reflectometry skin-lesion diagnostic study, vhich aims to use a newly developed bioengineering device to identify physiological features that reflect the athology of skin lesions. "he statistical methods we investigate can be divided into five primary research goals: . To develop and evaluate marginal estimation methods under general nonparametric and semiparametric egression models with flexible data collection designs. 2. To develop and evaluate semiparametric methods when a major covariate is a latent variable in a secondary mixed model. 3. To develop and evaluate efficient semiparametric methods to accommodate incomplete data using estimating equation and imputation-maximization approaches. 4. To develop and evaluate nonparametric and semiparametric generalized linear model approaches for ;orrelated data with functional covariates and a scalar response. 5. To develop and evaluate semiparametric standardization procedures for microarray data with a large proportion of outlying observations. The major focus of this proposal is the development of intuitive, efficient and computationally feasible methods without imposing unnecessary parametric assumptions. We expect our effort on these interesting biological studies to have significant impact on advancements in cancer research.