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

在统计科学中，回归模型是一个数学公式，用于描述响应变量和一组协变量之间的关联。传统的回归分析假设关于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，它要求样本容量大于协变量的数量。然而，这些假设在模拟真实的数据时并不总是现实的。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，由于截断和删失，可能无法完全观察到响应;协变量可能是高维的，并且是分组的。该提案的目的是开发所谓的新的半参数回归模型来处理这些问题，并为与加拿大人的经济和健康有关的科学问题提供解决方案。这些回归模型中的响应可以是患者的一生、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、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，其中一些基因可能与疾病有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，从而找到治疗疾病和改善生活质量的有效治疗方法是非常重要的。 除了拟议研究的理论创新外，从实践的角度来看，研究成果将非常有用和有吸引力。例如，在我的一个关于加拿大健康与老龄化研究数据分析的合作项目中，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。我们的初步分析，使用新的统计方法，将信息从截断时间分布提供了更准确的结果表明，血管性痴呆的老年人有更差的生存比阿尔茨海默氏症。我们的研究结果将回答痴呆对预期寿命的影响，并帮助流行病学家和患者更好地了解和治疗疾病。 拟议的方案提供了机会，在各级高素质的人员（HQP）的培训，无论是通过基本的方法研究或合作项目。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，使加拿大人能够轻松和广泛地获得。

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.