Empirical Likelihood For The Proportional Hazards Mixed-Effects Model With Cluster Data

Proportional hazards mixed-effects model is an extension of cox's frailty proportional hazards regression model.It has been widely used in survival analysis,compared with other survival analysis model,proportional hazards mixed-effects model is simple,intuitive and easy to understand,and it has natural clustering structure.In many epidemiological studies,In order to study the relationship between the risk factors and the incidence of disease,the collected data as a unit in each family,when we analyze the survival data,we usually make each family as a group,then we get the clustering data.Due to the limitation of the observation time,as well as the individual differences of observation object entry or exit,and any other reasons,the survival of data usually censored,thus this article mainly discusses in the condition of right censored data,the empirical likelihood for the proportional hazards mixed-effects model with cluster data,the main structure is as follows:First,we described the cox's proportional model,the cox's frailty proportional hazards regression model and proportional hazards mixed-effects model.Second,in the presence of censored data,reference the nonparametric likelihood method of cox's frailty proportional hazards regression model and partial likelihood method of cox proportional hazards models,constructs partial likelihood function of proportional hazards mixed-effects model,then constructs the asymptotically normal confidence interval.Again,in the condition of right censored data,we use the empirical likelihood to inference the proportional hazards mixed-effects model with cluster data,reference the empirical likelihood method of cox's proportional hazards model,constructs the empirical likelihood ratio function of unknown parameters in the model,and prove the asymptotic distribution of chi-square distribution,and then construct the confidence interval of unknown parameters.Finally,through the data simulation,at the same level,compared the confidence interval coverage probability and the length of confidence interval respectively in the empirical likelihood method and the normal approximation method,the simulation results show that the empirical likelihood method(EL)are better than the normal approximation method(NA),and coverage probability of the empirical likelihood method is closer to the confidence level,it is more accurate when the censored proportion is heavy and sample size is small.Therefore,the empirical likelihood method is effective and feasible for the proportional hazards mixed-effects model with cluster data.