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与一组协变量之间关联的数学公式。传统的回归分析假设响应变量的数据可以被完整记录并且数学公式被明确定义；它要求样本量大于协变量的数量。然而，这些假设在对真实数据建模时并不总是现实的。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，反应可能无法得到充分观察；协变量可以是高维的并且是分组的。该提案的目的是开发所谓的新半参数回归模型来处理这些问题，并为与加拿大经济和健康相关的科学问题提供解决方案。这些回归模型中的响应可能是患者的一生、个人的收入和保险公司的索赔；协变量可以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，需要测量数千个基因，其中一些可能与疾病相关并影响患者的一生，此外，基因表达的测量可以按基因通路进行分组。为了延长患者的生命，通过我们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并提高生活质量非常重要。 ******除了拟议研究的理论创新之外，从实践的角度来看，研究成果也将非常有用和有吸引力。例如，在我的一个合作项目中，对加拿大健康与老龄化研究的数据进行分析，这是最大的痴呆症流行病学研究之一，其中生存时间被左截断和右删失。与阿尔茨海默病相比，血管性痴呆的研究还不够深入。我们使用所提出的新统计方法结合截断时间分布的信息进行初步分析，提供了更准确的结果，表明患有血管性痴呆的老年人比患有阿尔茨海默病的老年人的生存率更差。我们的结果将给出痴呆症对预期寿命的影响的答案，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研究或合作项目为各级高素质人才（HQP）的培训提供机会。此外，通过在高影响力和开放获取期刊上发表研究论文以及在 R 和 GitHub 等平台上分发计算机软件，加拿大人将可以轻松、广泛地获取我们的研究成果。