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

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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.