Theory and Methodology for Semiparametric Linear Models with Censored Data

与著名的考克斯模型不同，直接通过某些变换对生存时间建模越来越受到从业者的欢迎，因为它假设了响应变量和协变量之间的简单关系，并且具有易于解释的参数。作为一个特例，半参数加速失效时间模型将失效时间用对数变换，在过去的十年中得到了广泛的研究。这些半参数线性变换模型现有的挑战包括半参数有效估计，渐近理论与更现实的条件，可能会导致良好的性能，生存时间预测，可测性问题的随机积分公式的结果依赖加权估计方法，和高维数据分析。研究者提出了新的方法来解决半参数线性变换模型中出现的问题。渐近理论将使用现代经验过程理论来证明。所有提出的方法的数值实现将基于那些发达的离散估计函数的算法或平滑的目标函数，其中的无穷维参数近似的平滑估计的牛顿-拉夫森方法。为了提高预测能力，更灵活的转换被认为是高维数据的问题。惩罚方法将被研究，以获得同时变量选择和生存时间prediction.Statistical模型考虑在这个项目中有重要的应用在广泛的学科，如生物学，医学，健康研究和工程。这项研究的动机特别是多队列研究的妇女的生殖生活分期，其中预测绝经年龄是主要的兴趣，并通过密歇根州卵巢癌和肺癌研究，寻找相关基因和良好的模型预测患者的生存使用基因表达数据。它将提供更有效地使用数据并产生更精确预测的方法。它还将允许研究人员为研究生的高级生存分析和半参数模型课程添加更全面的统计结果。拟议的研究活动将激励研究生成为能够从事基础统计研究的独立研究人员。

Instead of modeling the hazard function for censored survival data as the famous Cox model does, modeling the survival time directly by certain transformation becomes increasingly appealing to practitioners because it postulates a simple relationship between the response variable and covariates with easily interpretable parameters. As a special example, the semiparametric accelerated failure time model that transforms the failure time by logarithm has been studied extensively in the past decade. Existing challenges for those semiparametric linear transformation models include semiparametric efficient estimation, asymptotic theory with more realistic conditions that may lead to good properties for survival time prediction, a measurability issue in the stochastic integral formulation for the outcome-dependent weighted estimating methods, and high-dimensional data analysis. The investigator proposes new methods to tackle those emerging issues in the semiparametric linear transformation models. Asymptotic theories will be proved by using the modern empirical process theory. Numerical implementations of all the proposed methods will be based on either those well developed algorithms for discrete estimating functions or the Newton-Raphson method for smooth objective functions in which the infinite-dimensional parameter is approximated by a smoothing estimator. To enhance the predicting ability, more flexible transformations are considered for problems with high-dimensional data. Penalized method will be investigated in order to obtain simultaneous variable selection and survival time prediction.Statistical models considered in this project have important applications in a wide spectrum of disciplines such as biology, medicine, health studies, and engineering. The proposed research is particularly motivated by the multi-cohort study for the women's reproductive life staging in which the prediction of age at menopause is of major interest, and by the Michigan ovary cancer and lung cancer studies that look for relevant genes and good models for predicting patients' survival using gene expression data. It will provide methods that use data more efficiently and yield more precise prediction. It will also allow the investigator to add more thorough statistical results to the courses of advanced survival analysis and semiparametric models for graduate students. The proposed research activities will motivate graduate students to become independent researchers who are able to engage in fundamental statistical research.