Parametric Estimation Inference With Missing Covariates Under Additive Risk Models

Survival analysis has been used in many fields such as biology,public health,medical engineering,epidemiology,and reliability statistics.It is a statistical method to study the relationship between covariates and survival data by establishing survival models.The additive risk model It is an important survival analysis model in survival analysis.In practical application analysis,the problem of missing data often occurs.In the case of missing data,the estimation of model parameters may cause deviations.Therefore,through the survival analysis theory,using the inverse method The probability weighted estimation method and the Bayesian estimation method are used to statistically derive the parameters of the additive risk model with missing covariates,estimate the model parameters,and explore the statistical significance and practicality of the estimation effect of the two methods.The first chapter introduces the background of survival analysis,the theory and practical application of the study of missing covariates,summarizes the previous research,and explains the purpose and significance of this research in combination with the current research.The second chapter briefly introduces censored data,missing data mechanism,semiparametric models commonly used to solve survival analysis,several commonly used methods for dealing with missing data,and Bayes’ theorem and other related theoretical knowledge of survival analysis.The third chapter gives the description and assumptions of the additive risk model,introduces the parameter estimation function expression of the additive risk model,uses the inverse probability weighting method to adjust the estimation function expression of the additive risk model,and modifies the estimation function of the additive risk model to obtain The expression of the inverse probability weighted estimation function with missing covariates proves the asymptotic normality of the inverse probability weighted estimator under certain regularity conditions.The numerical simulation is carried out by the ahza package of the R software,which is relatively simple.The estimation effect of the weighting method and the inverse probability weighting method verifies the effectiveness of the inverse probability weighting estimation method under the right-censored data.It has better estimation results in the case of limited samples and improves the estimation efficiency.The results show that the estimation effect of the inverse probability estimation method is better than that of the complete data analysis method.According to the significant P value,it shows that the Gpd-1 phenotype and virus content have a significant effect on the occurrence of mouse leukemia,which fully proves the inverse probability weighting.The estimation method is statistically significant and practical.In the fourth chapter,the survival function,hazard function and distribution function in survival analysis are given.Assuming that the survival time of the research individual obeys the exponential distribution,the hazard rate function and the survival function with the additive risk model are obtained,and the right censoring is obtained.Likelihood function for an exponentially distributed additive risk model under the data.Assuming that the missing mechanism is missing at random,a distribution model for the missing covariates is constructed,a Bayesian estimation model for additive risk with missing covariates is constructed,and the joint is obtained by Bayes’ theorem The posterior distribution density function,the conditional posterior density function of each parameter is obtained according to the posterior likelihood function,the conditional posterior density function of each parameter is sampled by the MH algorithm,and the deviation(Bias)and standard deviation(SD)of the sampling sample are calculated.),mean square error(MSE)and95% confidence interval coverage(CP),the simulation results show that the estimated deviations(Bias)of the parameters under the distribution with missing covariates are all less than 0.1,and the standard of parameter estimation The differences are relatively small,indicating that the Bayesian parameter estimation of the additive risk model is effective,and the Bayesian estimation method is feasible.