| 区间删失数据Cox回归模型的参数估计 |
| Alternative Title | Parametric Estimation of Cox Regression Model for Interval-Censored Data
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| 赵瑞 |
| Thesis Advisor | 赵学靖
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| 2014-05-31
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 区间删失数据
Cox比例风险模型
坐标下降法
变量选择
Lasso
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| Abstract | 生存分析中，Cox 比例风险模型因其参数估计不依赖于特定分布、可以描述生存时间与其影响因素的关系而被广泛使用。在实际问题中，很多时候获得的生存时间样本数据信息并不完全，我们把这类不完全数据称为删失数据，如果仅知生存时间处于某区间内而无法得知其准确死亡时间，该类数据为区间删失数据。本文主要研究区间删失数据情形下，基准生存函数为指数型和 Weibull 型的 Cox 比例风险模型参数的极大似然估计，并用坐标下降法进行数值求解。当协变量个数过多时不但会影响模型的稳定性，也不利于模型的解释，所以变量选择就成为建模过程中至关重要的步骤，本文进一步对上述研究中协变量为高维的情形运用 Lasso方法进行了变量选择，通过数据模拟展示了参数估计效果和变量选择结果。 |
| Other Abstract | Cox's proportional hazard model has been widely used in survival analysis because of its independence on a particular distribution in its parameter estimation, and the good description of the relationship between the survival time and its related factors. Most often, the sample of survival data can not provide completely information, such samples are called as censored data. When the survival times lie in a time interval rather than exactly observed, we call this sample as interval censored-sample. This paper mainly studies the maximum likelihood estimation of the parameters of Cox's proportional hazard model when the sampled data are the interval censored data and survival functions are either exponential distributed or Weibull distribute. The parameters are estimated upon using coordinate descent algorithm. In addition, this paper devotes the covariate variable selection in the high dimensional case, including too many variables in the model can affect the stability and the explanation of the model, variables selection procedure are proceeded by using the Lasso method. Simulation results illustrate the performance of the parameters estimation and covariate variables selection. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224786
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
赵瑞. 区间删失数据Cox回归模型的参数估计[D]. 兰州. 兰州大学,2014.
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