Measurement Error, Missing Data and Semiparametrics

描述（由申请人提供）：该提案反映了我们对解决一般回归设置中的测量误差、不完整数据和/或功能（曲线）数据问题的持续兴趣。所提出的研究课题自然是从各种重要的研究中产生的。这些研究包括（i）结肠癌肿瘤发生项目，其包括一系列在细胞水平上研究结肠癌肿瘤发生的实验，（ii）部分降解的mRNA粪便微阵列实验，其中研究人员打算从粪便流中脱落的结肠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，和（iii）光谱斜入射反射计皮肤病变诊断研究，旨在使用新开发的生物工程设备来识别反映皮肤病变病理学的生理特征。"我们研究的统计方法可以分为五个主要研究目标：发展和评估一般非参数和半参数回归模型下的边际估计方法，并采用灵活的数据收集设计。2.当主要协变量是次要混合模型中的潜变量时，开发和评价半参数方法。3.开发和评估有效的半参数方法，以适应不完整的数据，使用估计方程和插补最大化方法。4.开发和评估非参数和半参数广义线性模型方法;或具有函数协变量和标量响应的相关数据。5.开发和评估半参数标准化程序的微阵列数据与大比例的离群观察。该提案的主要重点是开发直观，高效和计算可行的方法，而不施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对癌症研究的进步产生重大影响。

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.