Theory and Methodology for Semiparametric Linear Models with Censored Data

不像著名的Cox模型那样，对剔除的生存数据进行风险函数建模，而是通过某种转换直接对生存时间进行建模，因为它假设了响应变量与具有易于解释参数的协变量之间的简单关系，因此越来越受到实践者的欢迎。作为一个特殊的例子，将失效时间按对数变换的半参数加速失效时间模型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面临的挑战包括半参数有效估计、具有更现实条件的渐近理论（可能导致较好的生存时间预测性能）、结果相关加权估计方法的随机积分公式中的可测量性问题以及高维数据分析。研究人员提出了解决半参数线性变换模型中出现的问题的新方法。用现代经验过程理论证明渐近理论。所有提出的方法的数值实现将基于那些离散估计函数的良好发展算法或光滑目标函数的牛顿-拉夫森方法，其中无限维参数由平滑估计器近似。为了提高预测能力，对高维数据问题考虑了更灵活的转换。为了同时获得变量选择和生存时间预测，将研究惩罚方法。本项目中考虑的统计模型在生物学、医学、健康研究和工程学等广泛学科中具有重要的应用。提出的研究特别受到妇女生殖生活分期的多队列研究的推动，其中绝经年龄的预测是主要兴趣，以及密歇根卵巢癌和肺癌研究寻找相关基因和使用基因表达数据预测患者生存的良好模型。它将提供更有效地利用数据并产生更精确预测的方法。它还将允许研究者在研究生的高级生存分析和半参数模型课程中添加更彻底的统计结果。建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.