Variable Selection Of Cox Proportional Hazards Model Based On Length Deviation Data

Cox Proportional Hazard model is one of the most widely used models in survival analysis,which has been widely used in various fields.There are a lot of literature on the variable selection of Cox model.However,in practice,it is sometimes encountered that an individual can only be observed if certain preconditions are met.In this case,the data obtained is called truncation data.When the truncation variables are uniformly distributed,the observed survival time is called the length deviation data.This paper mainly studies the variable selection of Cox proportional hazard model with length bias data.Because of the length-bias data,the classic partial likelihood function is no longer applicable.Based on the combination of the partial partial likelihood function and the idea of Adaptive Lasso,this paper presents a variable selection method for the Cox proportional hazard model under length-bias data.In order to solve the estimation equation,this paper uses the improved Shooting algorithm to obtain the value of (?)_j.To ensure the effect of variable selection,the GCV method is used to select the adjustment parameter ?.Through a large number of simulation calculations,the variable selection effect and parameter estimation accuracy of the given method are demonstrated,and the Adaptive Lasso method is compared with the Lasso and SCAD methods.Through simulation calculations under different dimensions,different sample sizes,and different censoring rates.We find that the Adaptive Lasso method is superior to the Lasso and SCAD methods in both variable selection and non-zero parameter estimation accuracy,and has a better variable selection effect.As an example application,we also use the proposed method for Oscar data Set to study the relationship between the lifetime of these Oscar-winning actors and whether they won the prize and other influencing factors.Since the actor's survival time is only observed when the actor's death time is longer than the time of the first nomination,this data set belongs to length-biased data.The results show that the proposed method performs well,further confirming the effectiveness of the proposed method.Theoretically,we have proved the consistency and Oracle property of Adaptive Lasso method under length-bias data.Therefore,the study of variable selection of Cox model under length deviation data has certain theoretical value and practical significance.