Generalized semiparametric odds ratio models

在这个研究项目中，研究人员有两个目标要实现。第一个目标是发展一类新的半参数优势比模型的统计推断理论，该模型同时包括广义线性模型和Cox回归模型作为特例。第二个目标是应用这类模型来解决一些在应用中具有重要意义的理论问题。这些应用包括：(1)解决有偏抽样设计中的参数可辨识性、估计和推论问题，研究疾病与基因和环境因素的相关性；(2)引入一种新的检验广义线性模型拟合优度的方法；(3)发展一种新的灵活的半参数方法，用于复杂相关结构的多变量密度估计和生存分析。灵活且易于解释的随机模型对于从复杂结构的数据中提取信息非常有用。这类数据通常是在探索疾病和其他社会经济问题的原因的研究中收集的。研究人员提出了一类新的模型来对这些数据进行统计分析。这项研究的结果将在各种科学领域有广泛的应用。当应用于流行病学研究时，这项研究的结果将能够促进设计更强大的统计测试，以检测疾病的遗传和环境原因。当应用于社会学研究时，这项研究的结果将能够有助于理解复杂的社会经济问题的根本原因，从而能够找到更好的解决问题的办法。

The investigator has two objectives to accomplish in this researchproject. The first objective is to develop theory of statistical inference for a new class of semi-parametric odds ratio models thatinclude both the generalized linear model and the Cox regression model as special cases. The second objective is to apply this class of models to solve a number of theoretical problems that are of importance in applications. These applications include (1) addressing issues in parameter identifiability, estimation, and inference in biased sampling designs in studying the association of a disease with gene and environment factors, (2) introducing a new approach for testing goodness of fit of generalized linear models, and (3) developing a new flexible semi-parametricprocedure for multivariate density estimation and survival analysis with complex dependence structures.Flexible and easily interpretable stochastic models are very useful in extracting information from data with complex structures. Such data are often collected in studies exploring the causes of diseases and other socio-economic problems. The investigator proposes a new class of models for the statistical analysis of such data. Results from this research will have broad applications in a variety of scientific fields. When applied to epidemiological studies, results from this research will be able to facilitate the design of more powerful statistical tests for detecting genetic and environmental causes of disease. When applied to sociological studies, results from this research will be able to facilitate the understanding of underlying causes of complex socio-economic problems so that better solutions to the problems can be found.