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: $ 4.08万
• 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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759047
• 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，回归模型是一种数学公式，用于描述响应变量与一组协变量之间的关联。传统的回归分析假设可以完全记录有关响应变量的数据，并且明确定义了数学公式；它要求样本量大于协变量数量。但是，这些假设在建模实际数据时并不总是现实的。如果违反了这些假设中的一个或多个，那么许多现有的统计分析方法将不再有用。例如，由于截断和审查，可能无法完全观察到响应。协变量可能是高维且分组的。该提案的目的是开发所谓的新的半参数回归模型来解决这些问题，并为与加拿大人的经济学和健康有关的科学问题提供解决方案。这些回归模型中的回答可能是患者的一生，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治疗方法，即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，测量了数千种基因，其中一些基因可能与疾病有关，并影响患者的寿命，此外，基因表达的测量可以通过基因途径进行分组。为了延长患者的寿命，通过我们的新回归模型识别和选择这些重要的个体基因和基因组非常重要，然后找到一种有效的治疗方法来治愈疾病并改善生活质量。除了提出的研究的理论创新外，从实际的角度来看，研究成果将非常有用且具有吸引力。例如，在我从加拿大健康和衰老研究的数据分析上进行的一个协作项目中，这是最大的痴呆流行病学研究之一，其中生存时间左截止和右审查。与阿尔茨海默氏症相比，血管性痴呆症已被研究。我们使用拟议的新统计方法的初步分析，该方法合并了截断时间分布中的信息提供了更准确的结果，以表明血管性痴呆的老年人的生存率要比患有阿尔茨海默氏症的老年人差。我们的结果将为痴呆症对预期寿命的影响提供答案，并帮助流行病学家和患者更好地理解和治愈疾病。拟议的计划为通过基本的方法论研究或协作项目在各个层面上培训高素质人员（HQP）提供了机会。此外，通过发表高影响力和开放访问期刊的研究论文，并将计算机软件分发在R和GitHub等平台上，加拿大人将轻松且广泛地访问我们的研究成果。