几种变量选择方法在Cox模型中的应用

发布时间：2018-07-01 09:44

本文选题：Lasso + Adaptive　；参考：《广西大学》2015年硕士论文

【摘要】：在生存分析中,Cox模型是处理生存数据的经典模型.随着大数据的盛行,人们面对高维、强相关生存数据的机会越来越多.如何克服传统Cox模型不能处理上述生存数据的缺陷,已成为统计学界共同关注的热点.为解决这一问题,本文将变量选择中比较重要的两种方法应用于Cox模型中,即Elastic Net方法和Adaptive Elastic Net方法.具体研究内容及结果如下：一方面,由于Elastic Net方法能有效处理高维小样本、强相关变量组数据,本文将其运用于Cox模型的变量选择中,探讨Cox模型下Elastic Net估计的组效应性质,证明得到Elastic Net方法能将强相关变量组中的变量全部选入模型,即具有组效应性质.通过数值模拟,验证了Elastic Net估计具有组效应性质,而Lasso方法无此功效.通过具体实例,肯定了ElasticNet方法运用于Cox模型的可行性,验证了Elastic Net方法的拟合效果和预测能力均优于逐步法,表明了与Elastic Net方法结合后的Cox模型优于传统Cox模型.另一方面,由于Adaptive Elastic Net方法对零变量的估计优于Elastic Net方法,本文将Adaptive Elastic Net方法运用于Cox模型的变量选择中,探讨Cox模型下Adaptive Elastic Net估计的组效应性质及Oracle性质,证明得到Adaptive Elastic Net方法能将强相关变量全部选入模型,且对零变量的处理更准确,即具有组效应性质及Oracle性质.通过数值模拟,验证了在拟合效果和精确度方面,Adaptive Elastic Net方法优于Lasso方法、Adaptive Lasso方法和Elastic Net方法.
[Abstract]:Cox model is a classical model for dealing with survival data in survival analysis. With the prevalence of big data, there are more and more opportunities for people to face high-dimensional and strongly related survival data. How to overcome the shortcomings of the traditional Cox model which can not deal with the above survival data has become a common concern in the field of statistics. In order to solve this problem, two important methods of variable selection are applied to Cox model, i.e. Elastic net method and Adaptive Elastic net method. The specific contents and results are as follows: on the one hand, Elastic net method can effectively deal with high-dimensional, small-sample and strongly correlated variable set data. In this paper, we apply it to the selection of variables in Cox model, and discuss the group effect properties of Elastic net estimation under Cox model. It is proved that the Elastic net method can select all the variables in the strongly correlated variable group into the model, that is, it has the property of group effect. Numerical simulation shows that Elastic net estimation has group effect property, but Lasso method has no effect. The feasibility of applying Elastic net method to Cox model is confirmed. The fitting effect and prediction ability of Elastic net method are better than that of step by step method. It is shown that the Cox model combined with Elastic net method is superior to the traditional Cox model. On the other hand, because Adaptive Elastic net method is superior to Elastic net method in estimating zero variables, this paper applies Adaptive Elastic net method to variable selection of Cox model, and discusses the group effect property and Oracle property of Adaptive Elastic net estimation under Cox model. It is proved that all strongly correlated variables can be selected into the model by Adaptive Elastic net method, and the processing of zero variables is more accurate, that is, it has group effect property and Oracle property. Numerical simulation shows that adaptive Elastic net method is superior to Lasso method and adaptive Lasso method and Elastic net method in fitting effect and accuracy.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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