Empirical Likelihood Inference For Proportional Risk Models With Dependent Covariates Under Interval Censored Data

COX proportional risk model,which is the most commonly used method in survival analysis,has been widely used in chronic epidemiology currently,while parametric proportional risk regression model based on various distributions has been applied in biology and medicine.Engineering science also plays an important instrumental role in sociology,psychology,economics,actuarial insurance and reliability.At the same time,the distribution of our survival time satisfies the generalized exponential distribution,and the risk rate function is flexible and can be used for modeling and analysis of many types of hazard rate data.Of course,the interval censored time data also has a relatively better and more flexible analysis results,and has important applications in many fields such as life test and reliability research.In this paper,a semi-parametric regression problem for intervaldependent censored data under proportional risk model is proposed.The confidence intervals of unknown parameters are constructed by empirical likelihood method,and the results are compared by numerical simulation.Firstly,this paper analyzes the current situation of COX proportional risk model with dependent interval deletion,and briefly introduces COX proportional risk model,interval censored data processing method,unknown parameter estimation method and empirical likelihood method in the model.Secondly,an implicit function method is used to process the interval censored data,and then the unknown parameters in the proportional risk model under interval censored data are estimated by a method similar to the generalized estimation equation.Finally,the expression of the confidence interval of unknown parameters in the model is derived by empirical likelihood method.Finally,the regression parameters obtained by the above estimation methods are analyzed by simulation experiments.Under the same estimation method,the coverage probability increases gradually and the standard error decreases with the increase of sample size.When the sample size n is the same,the smaller the censored ratio CR is,the smaller the confidence interval length of the two methods is,and the coverage probability is close to the confidence level,which is in accordance with the theoretical research results.In the case of the same sample size and the same censored ratio CR,the coverage probability obtained by the empirical likelihood method is close to the confidence level,because in the maximum likelihood estimation method,The standard error of regression parameters will be biased with the widening of confidence interval.In general,almost all simulation results,empirical likelihood method(EL)performance is better.