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Cox比例风险模型在生存分析中扮演着重要的角色，它能够利用风险函数研究变量与生存函数间的关系，初步处理存在删失情况的生存数据，但实际生活中的数据通常不满足Cox比例风险假定。针对这类数据，引入部分线性可加Cox模型，实现对时依协变量的变量选择研究。本文主要研究内容分为以下三部分：

1. 通过B-样条曲线拟合部分线性可加Cox模型中的非参数部分，将模型中未知分量函数选择问题转变为处理线性组合中选择系数组的问题，实现对部分线性可加Cox模型的样条拟合。
2. 针对部分线性可加Cox模型中的删失生存数据引入双层变量选择方法，其中协变量自然分组。与组变量选择相比，实现在选定的组内同时进行组选择和个体变量选择，提高模型估计精度。
3. 通过模拟分析对比组变量选择方法和双层变量选择方法在五类指标下的性能，验证了双层变量选择方法在部分线性可加Cox模型中的有效性。分别引入两类不同的癌症数据集，结果表明双层变量选择方法筛选出的变量与存活时间相关度最高，即对攻克癌症疾病有现实意义。

研究表明双层变量选择方法在部分加性Cox模型中的预测误差优于组变量选择方法，引入的两个数据集都体现了双层变量选择方法的有效性。

Cox proportional risk model plays an important role in survival analysis. It can use risk functions to study the relationship between variables and survival functions, and initially process survival data with censoring. However, data in real life often do not meet the Cox proportional risk assumption. For this type of data, a partially linear additive Cox model is introduced to achieve variable selection research for time-dependent covariates. The main research content of this article is divided into the following three parts:

(1)By fitting the nonparametric part of a partially linear additive Cox model with a B-spline curve, the problem of selecting unknown component functions in the model is transformed into the problem of dealing with the selection of system arrays in linear combinations, and spline fitting of partially linear additive Cox models is realized.

(2)Bi-level variable selection method is introduced for censored survival data in partially linear additive Cox models, where covariates are naturally grouped. Compared with group variable selection, group selection and individual variable selection can be performed simultaneously within the selected group, improving model estimation accuracy.

(3)By comparing the performance of the group variable selection method and the two-level variable selection method under five indicators through simulation analysis, the effectiveness of the two-level variable selection method in a partially linear additive Cox model was verified. Two different types of cancer data sets were introduced, and the results showed that the variables screened by the two-level variable selection method had the highest correlation with survival time, which was of practical significance in tackling cancer diseases.

Study has shown that the prediction error of the two-level variable selection method in the partially additive Cox model is better than that of the group variable selection method. The two data sets introduced reflect the effectiveness of the two-level variable selection method.