The Proportional Structure Of The Covariate In The Mixed Cure Rate Model With Penalization

With the development of drugs and medical means,the cure rate and survival time of patients with malignant tumors and cardiovascular diseases have been significantly improved.Early detection of the disease and accurate and effective treatment is the key to improve the cure rate,prolong the survival time and reduce the death rate.In clinical and epidemiological statistical studies,survival time data are mainly derived from two types of patients:those who are susceptible to relapse?called susceptible patients?and those who have recovered from recurrence?called immune patients?.The general survival analysis model usually assumes that all subjects will eventually experience recurrence events to study the survival time distribution,but ignores the situation of immune patients in the population,so it is not suitable for the study analysis with mixed data of cured patients.The"mixed cure rate model"proposed by Boag for the first time is a two-part model that not only allows the occurrence of cure probability,but also simulates the survival time distribution of susceptible population.The"mixed cure rate model"is mainly used to estimate the cure rate of patients and to look for the distribution function of survival time of susceptible patients.At present,relevant researches do not pay enough attention to the influence of covariates in the model,which provides a new idea for the research in this paper.In this paper,the penalty function is used to improve the structural effect of the covariate in the mixed cure rate model,and the model accuracy is effectively improved through the verification of numerical example.In this paper,the author focuses on the effect of covariates on the proportion structure in the mixed cure rate model,which mainly includes the following parts:Firstly,a mixed cure rate model with covariates subject to generalized exponential distribution was established,and the maximum likelihood estimation was solved iteratively by EM algorithm and Newton-Raphson algorithm,and the estimated values of the parameters in the model were obtained.Then,a penalty mechanism is used to identify the proportional structure of the covariates in the two-part model.The concept of the two-part model and the proportional structure of co-variables are introduced in detail.By solving the model parameters and judging the value of parameters and parameter components,the proportional structure of the co-variables in the two-part model is identified,and the detailed mathematical model and corresponding algorithm are given.The strict statistical properties are established and the theoretical proof is given,which provides a theoretical basis for the proposed method.Finally,the structural effects of covariates on the mixed cure rate model were improved by setting penalty terms.According to the characteristics of covariate data,the author developed a new Ridge-L₂ penalty function and proved it theoretically.Finally,through actual data?TCGA?,it is verified that setting penalty item can effectively improve the structural effect of covariates and the accuracy of parameter estimation.At last,the paper summarizes the whole paper and looks forward to the future research direction.