Semi-Parametric Estimation For Recurrent Event Data With Information Censoring

Recurrent event data with information censored events widely exists in medical and biological research.Examples include the time of patients repeatedly experiencing clinical events and the time of repeated asthma attacks.Currently,scholars have studied the recurrent event data with information censored the research is mainly based on the Poisson assumption of the recurrence event process and the condition of the distribution parameter assumption of the frailty variable,and the estimation results are easily affected by the assumption conditions.In addition,most of the research methods proposed by scholars require that the covariates are independent of time,and the relationship between the recurrence event data are independent between each other,which may not be satisfied in practical applications.This paper mainly studies the robust estimation method of semi-parametric frailty model for recurrent event data with information censored.In the first chapter,we describe the background significance and current research status of this paper,which mainly introduces the existing research methods of multivariable survival time model,marginal modeling and fragile model of recurrent event data.In the second chapter,a semi-parametric frailty model is proposed.We do not need to assume the distribution of frailty variables and the Poisson process hypothesis of recurrence process.We use the method of counting process intensity function to obtain the estimation equation of parameters,discuss the estimation performance of different weight functions,and obtain the optimal estimation value of regression parameters.We prove the consistency and asymptotic normality of the proposed estimators in regular conditions,and numerical simulations show that the proposed model and method are reasonable and optimality.In the third chapter,a semi-parametric frailty model with time independent covariable and time covariable function is proposed.Our model does not rely on the distribution hypothesis of frailty variables and the Poisson hypothesis of recurrent event processes,and allows the deletion time to be associated with recurrent event processes through unobserved vulnerabilities.We propose a new semi-parametric estimation method.By constructing a transformed random process,we obtain the regression parameters of the time covariable function estimated by the martingalelike zero-mean random process,and solve the estimation equation derived from the transformed random process.The estimated values of time independent covariable regression parameters are obtained.We prove the consistency and asymptotic normality of the proposed estimators in regular conditions,and numerical simulations show that the proposed model and method are reasonable and optimality.In the four chapter,we use recurrent event data generated by pooled treatment to propose parametric models with exponential and multiplicative effect covariates.We interpret frailty variables as potential shared factors that affect the recurrence process of individuals,and allow skewness or multi-peak distribution.In this paper,the common frailty variables are regarded as model parameters,the categories of individuals are regarded as potential variables,and the parameters are estimated by a method similar to Gaussian mixture model.We prove the consistency and asymptotic normality of the proposed estimators in regular conditions,and numerical simulations show that the proposed model and method are reasonable and optimality.