Measurement Error, Missing Data and Semiparametrics

描述（由申请人提供）：该提案反映了我们在解决一般回归设置中的测量误差，相关数据和纵向/功能（曲线）数据问题方面的持续努力。随着技术的进步，每天都会产生更高维度和更复杂结构的数据。通常的做法是直接采用已应用于与这些新研究结构相似的数据的现有程序。然而，在某些情况下，这种做法可能导致无效的分析，甚至是误导性的结论。本提案的研究人员将把这种做法纳入测量误差建模的框架，并评估其有效性和潜在的缺点，在诱导不可忽略的偏差方面。学到的知识将允许研究人员开发合适的建模策略和新的统计方法，以最好地利用数据中嵌入的信息。提出的研究课题是在几项重要研究的基础上自然产生的。这些研究包括：(i)一项长期纵向研究，目的是研究终身风险暴露对生命后期健康状况的影响；(i)通过多种设备从不同背景的受试者中测量营养饮食指标和代谢物；（iii）为多平台基因组数据集，包括从同一受试者中同时收集的microRNA、多染色体和总mRNA，目的是调查结肠癌的肿瘤发生。（iv）光谱斜入射反射法皮肤病变诊断研究。这些研究项目背后的共同目标是增进对数据中所含信息的了解，从而加强疾病预防和早期发现。这一建议的主要重点仍然是发展直观和实用的模型，以及有效和计算上可行的方法，而不强加不必要的参数假设。通过一系列的目标，本研究项目将提供新的建模策略和统计方法，(i)利用两者

DESCRIPTION (provided by applicant): This proposal reflects our continuing efforts in solving problems of measurement error, correlated data and longitudinal/functional (curve) data in general regression settings. With the advancement in technology, data of higher dimension and more complex structures are generated daily. It is a common practice to directly adopt existing procedures that have been applied to data with similar structure to these new studies. Nevertheless, under certain circumstances, this practice could lead to ineffective analyses or even mis-leading conclusions. The investigators of this proposal will put such practice into a framework of measurement error modeling and evaluate its effectiveness and potential drawbacks in term of inducing non-negligible biases. The learned knowledge would allow researchers to develop suitable modeling strategies and new statistical methods that best exploit the information embedded in the data. The proposed research topics have arisen naturally from several important studies. These studies include (i) a long-term longitudinal study with the goal of studying effects of life-long risk exposure on health conditions later in life, (i) nutrition dietary mea- surements and metabolites, measured by multiple-devices, from subjects of diverse backgrounds, (iii) multi-platform genomic datasets, including microRNA, polysomal and total mRNA, collected from the same subjects at the same time for the purpose of investigating colon cancer tumorigenesis, and (iv) a spectroscopic oblique incidence reflectometry skin-lesion diagnostic study. A shared objective behind these research projects is to advance understanding of information embedded in the data and consequently to enhance disease prevention and early detection. The major focus of this proposal remains to be the development of intuitive and practical models as well as efficient and computa- tionally feasible methods without imposing unnecessary parametric assumptions. Through a series of aims, this research project will provide new modeling strategies and statistical methods that (i) utilize both modeling considerations and variable selection technique to identify suitable time period or effective locations where the changes or treatment effects exist; (ii) utilize a new mixture modeling strategy to flexible yet effectively describe distributions of features/variables of sub-populations, (iii) effectively borrow information through seemingly unrelated observations through correlations while maintain interpretability of outcomes, and finally (iv) utilize measurement-error modeling considerations to effectively link disease outcomes to latent features of correlated functional or longitudinal predictors. We expect our efforts on producing new statistical methods and applying them to important biomedical studies shall have significant impact on advancements in biological and medical research.