Research And Application Of Dantzig Selector Method In Semiparametric Model For Survival Analysis

With the rapid development of science and technology,the data and information obtained by people in various fields such as medicine,biology,economics,and industry have grown exponentially,and the data dimension has become higher and higher.Variable selection is a very effective means of extracting high-dimensional data information,however,the traditional variable selection method has certain defects.The Cox proportional hazard model is a semi-parametric model that occupies an important position in survival analysis,but its scope of application is restricted to low-dimensional data.In this paper,the Dantzig Selector method and the Adaptive Dantzig Selector method in the linear model are generalized to the Cox model,and their properties in the Cox model are studied.In this paper,the definition and solution ideas of regression parameter estimates for the variable selection methods(Lasso and related methods,Dantzig Selector method and Adaptive Dantzig Selector method)under the Cox model are given.The properties of Dantzig Selector method in Cox model are discussed,and it is proved that Adaptive Dantzig Selector method also has Oracle property in Cox model.In order to verify the validity of the theoretical study of the variable selection method under the Cox model,censored data of the Cox proportional hazard model were generated through numerical simulation.In this paper,we mainly study the variable selection ability of each method in the Cox model under the conditions of high-dimensional data and lowdimensional data,respectively considering the correlation and uncorrelation between variables.From the simulation results,the Dantzig selector method and the Adaptive Dantzig Selector method are better than other methods such as Lasso in low-dimensional data or high-dimensional data.The overall fitting effect is better.The validity and feasibility of the dimensional data.At the same time,the improved Adaptive Dantzig Selector method is better than the Dantzig selector method.