Improving The Estimation Efficiency Of The Mixture Cure Model

With the development of science and technology,therapeutic methods have improved,and various complex diseases can be diagnosed and treated,so there is a phenomenon of "long-term survivors" in survival data.In survival analysis,mixture cure models tend to characterize such mixed survival data.Based on the estimating equation method of the marginal proportional hazards mixture cure model proposed by Niu and Peng(2014),and the theoretical knowledge of the quadratic inference function proposed by Qu et al.(2000),we use the linear combination of basis matrices to represent the working correlation matrix in the model,and propose a new parameter estimation method.The new method not only considers the correlation within the same cluster of cluster survival data,but also avoids the estimation of the correlation coefficient and the scale parameter in the estimating equations.When there is a strong correlation between the survival time of the observed individual and the cure index,the estimator obtained by the new method is more stable than the existing method.Specifically,its variance estimation is significantly reduced,so as to achieve the purpose of improving the efficiency of the model.The structure of the article consists of four parts: the first part includes the research significance and research purpose of this paper;the second part combines the quadratic inference function method to construct a new parameter estimation equation for the mixture cure model,the modified EM algorithm is used to solve the estimation equations;we conduct simulation in the third part and use bootstrap variance method to evaluate the efficiency of the model;in the fourth part,we apply the new method to analyze kidney disease infection data and smoking cessation data,separately for illustration.