Variable Selection For Transformation Models Based On Quantile Regression With Missing And Censored Data

In the survival analysis,the proportional hazard model has been widely used in the medical field.It has many excellent properties.It is commonly used to estimate the survival time and evaluate the effects of various impact factors.It is a common method in survival analysis.The model also has certain limitations.At the same time,missing and censored data are often encountered in the process of medical data analysis.However,due to the difficulty in collecting medical data and the small sample size of medical data,the data is especially valuable.How to effectively use missing and censored data for medicine Survival analysis is of great significance,and there are many covariates related to medical data,which have certain sparsity.It is especially important to delete the variables that retain significant effects of invalid variables.The survival function has monotonous characteristics,and the general estimation method cannot satisfy the requirements.In view of the above practical problems,this paper generalizes the commonly used survival function model,relaxes the corresponding conditions,and obtains a more generalized transformation model.It is an extension of multiple survival models and has greater flexibility in clinical data analysis.Based on the generalized transformation model,this paper adopts the quantile regression method which has robust characteristics,and analyzes the data from multiple angles,and further adopts adaptive Lasso for variable selection,and finally monotonizes the regression survival function.Finally,it is theoretically proved that the model estimation has excellent asymptotic properties.In the numerical simulation,the paper estimates the model through three steps: the first step is to get a complete dataset by filling in the estimated values for the missing responses;the second step is to use the censored quantile for the completed datasets.In the regression method,in the estimation process,the two-step iterative method is used for local linear expansion estimation,and the adaptive Lasso is used for punishment.In the third step,the estimated transformation model is monotonized.Through simulation test analysis,it can be found that the model has excellent numerical fitting and variable selection ability when the missing and censored data account for a low proportion,and its ability increases with the increase of sample size.And when the missing and censored data account for a slightly high proportion,the model and method perform also well.This indicates that the estimation model in this paper has a good fitting ability and it has robust characteristics.In the case analysis part,the extended transformation model is applied to the survival analysis of patients with nasopharyngeal carcinoma in Shanxi Cancer Hospital.By setting the quantile regression variable selection for multiple survival points of the patient survival data,the model can effectively remove unrelated influence factors,and analyze the effects of different impact factors on the survival time of patients with different degrees.In summary,the estimation model and variable selection method based on missing and censored response variables can satisfy data sparseness with missing data and censored outcomes in real life medical survival analysis,and effectively analysis data.