生存分析中变系数模型的超高维协变量的筛选研究

Ultra-high dimensional data has become increasingly important in diverse fields of scientific research and technological development. In many censored data analysis, there may also involve ultra-high dimensional covariates, in which the effects of some important covariates on the censored time may vary with some other exposure covariate. In such case, we need to indentify the important covariates that have vary-coefficient effects on the censored time. Thus, this proposal is to establish the screening methods for vary-coefficient models in survival analysis with ultra-high dimensional covariates. Firstly, applicants plan to develop a new sure independence screening method based on some new marginal utility measure constructed from the marginal accumulative hazard function estimators, which can be obtained by the regularized survival analysis techniques after using B-splines approximation for the unknown vary-coefficients. Then the dimensionality of covariates can be reduced from ultra-high to a moderate scale through this sure screening method. Secondly, applicants will give the theoretical proof to verify that whether the proposed sure independent screening method has the sure screening property for even exponentially growing dimensionality. Finally, the methodology will be evaluated through extensive simulation studies and application to a real follicular lymphoma data set. Study of this proposal will provide beneficial attempt for the theoretical and application of the ultrahigh dimensional vary-coefficient models in survival analysis.

超高维数据在科学技术发展的各个领域里变得越来越重要。在许多生存数据的分析中，都涉及到超高维协变量，且某些重要的协变量对生存时间的效应可能会随着其他暴露变量而变化。在众多的协变量中，我们需要识别出那些对生存时间有变系数效应的重要协变量。因此，本项目拟建立不同的带有超高维协变量的生存时间的变系数风险模型。首先，采用非参数逼近的技术获得高维情形下累积危险率函数的估计，提出一种新的基于此估计的边际效用度量，以此来衡量每个协变量的重要程度，从而建立一种系统的变量筛选方法，达到将变量的维数从超高维降到一个适中的维数的目的。其次，申请者还计划证明提出的确保独立筛选方法在变量维数呈指数式增长的情况下具有确定筛选性质。最后，申请者拟通过大量的模拟研究及临床的滤泡性淋巴瘤的数据分析来验证我们提出的模型和方法的合理性与可行性。该项目的研究可为生存分析的超高维变系数模型的理论方法与应用研究提供有益的尝试。

本项目主要对超高维协变量下删失生存时间数据的变系数模型的确保独立筛选方法进行研究。对于带有超高维协变量的删失生存时间数据的变系数比例风险模型，提出了基于B-样条近似的边际累积危险率函数估计与非参数累积危险率函数的Aalen估计的差值构造的边际效用度量的确保独立筛选方法，证明了所提出的变量筛选方法的包括所提出的边际效用度量的合理性、确保独立筛选方法的确定筛选性质及对筛选变量子集个数的界的控制等理论性质，通过模拟计算分析了模型及方法的实际计算效果，并把所提出的模型和方法运用到实际的临床试验数据中，验证了提出模型及方法的合理性及可行性。受到本项目的资助，申请者基本完成了该项目中拟研究的第一个问题。作为其推广，研究二和研究三也将在后续工作中迅速完成。这些研究将为生存分析的统计研究带来新的理论成果，为临床医学、生物医学等应用提供更有价值的经验。此外，作为调整，若干生存分析领域的其他问题也被研究，相应工作都已顺利完成，在统计学国际学术期刊Computational Statistics and Data Analysis, Biometrical Journal, Acta Mathematicae Applicatae Sinica, English Series, Communications in Statistics- Simulation and Computation上各发表学术论文1篇。本项目资助了2名硕士生（其中1名硕博连读，1名已毕业工作）。本项目资助经费22万元，支出15.9702万元，各项支出基本与预算相符。剩余经费6.0298万元，剩余经费将用于本研究后续支出。