Model Selection and Efficient Estimation in Semiparametric Regression Models with Complex and High-Dimensional Data

复杂高维数据半参数回归模型的模型选择和高效估计

• 批准号: RGPIN-2018-06466
• 负责人: Lu, Xuewen
• 金额: $ 2.04万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=658040
• 关键词: Model; Selection; Efficient; Estimation; Semiparametric

In statistical science, a regression model is a mathematical formula used to describe association between a response variable and a set of covariates. Traditional regression analysis assumes that data concerning the response variable can be fully recorded and the mathematical formula is explicitly defined; it requires sample size to be larger than number of covariates. However, these assumptions are not always realistic in modelling real data. If one or more of these assumptions are violated, many existing approaches to statistical analysis cease to be useful. For example, responses may not be fully observed due to truncation and censoring; covariates may be high-dimensional and grouped. The aims of this proposal are to develop so called new semiparametric regression models to deal with these problems, and provide solutions to scientific problems which are related to Canadians' economics and health. The responses in these regression models could be a patient's lifetime, a person's income, and an insurance company's claim; the covariates could be a patient's genes and treatments received, a person's social and economic factors. For example, in genomics studies for cancer diseases, thousands of genes are measured and some of them might be related to a disease and affect patients' lifetime, besides, measurements of gene expression can be grouped by gene pathways. To prolong patients' lifetime, it is very important to identify and select those important individual genes and gene groups through our new regression models, then find an effective treatment to cure the disease and improve quality of life. ******In addition to the theoretical innovations from the proposed research, the research outcomes would be extremely useful and appealing from a practical point of view. For instance, in one of my collaborative projects on the data analysis from the Canadian Study of Health and Aging, one of the largest epidemiological studies of dementia, where survival time was left-truncated and right-censored. Compared to Alzheimer, vascular dementia has been understudied. Our preliminary analysis using the proposed new statistical method of incorporating information from the truncation time distribution provides more accurate results to show that the elderly people with vascular dementia have worse survival than those with Alzheimer. Our result will give an answer on the impact of dementia on life expectancy and helps epidemiologists and patients to understand and cure the diseases better. ******The proposed program provides opportunities for the training of highly qualified personnel's (HQPs) at all levels, either through fundamental methodological research or collaborative projects. Further, our research outcomes will be made easily and widely accessible to Canadians, through publishing research papers in high-impact and open-access journals and distributing computer software in platforms such as R and GitHub.

在统计科学中，回归模型是用于描述响应变量和一组协变量之间的关联的数学公式。传统的回归分析假设与响应变量有关的数据可以完全记录下来，并且明确定义了数学公式；它要求样本量大于协变量的数目。然而，在模拟真实数据时，这些假设并不总是现实的。如果这些假设中的一个或多个被违反，许多现有的统计分析方法就不再有用。例如，由于截断和审查，可能不能完全观察到响应；协变量可能是高维的和分组的。这项建议的目的是开发所谓的新的半参数回归模型来处理这些问题，并为与加拿大人的经济和健康相关的科学问题提供解决方案。这些回归模型中的反应可能是患者的一生、一个人的收入和保险公司的索赔；协变量可能是患者的基因和接受的治疗，一个人的社会和经济因素。例如，在癌症疾病的基因组学研究中，测量了数千个基因，其中一些可能与疾病有关并影响患者的生命，此外，基因表达的测量可以按基因途径进行分组。为了延长患者的寿命，通过我们的新的回归模型识别和选择那些重要的个体基因和基因组，然后找到有效的治疗方法来治愈疾病，提高生活质量是非常重要的。*除了拟议研究的理论创新之外，从实践的角度来看，研究成果将非常有用和有吸引力。例如，在我的一个合作项目中，来自加拿大健康和老龄化研究的数据分析，这是关于痴呆症的最大流行病学研究之一，生存时间被左截断和右审查。与阿尔茨海默病相比，对血管性痴呆的研究还不够深入。我们的初步分析使用了新的统计方法，结合了截断时间分布的信息，提供了更准确的结果，表明患有血管性痴呆的老年人的存活率比阿尔茨海默病患者更差。我们的结果将回答痴呆症对预期寿命的影响，并帮助流行病学家和患者更好地了解和治疗这种疾病。*拟议的计划通过基础方法学研究或合作项目，为各级高素质人员(HQP)的培训提供机会。此外，我们的研究成果将通过在高影响力和开放获取的期刊上发表研究论文，并在R和GitHub等平台上分发计算机软件，使加拿大人轻松和广泛地获得我们的研究成果。