Inference For Censored Quantile Regression Model Under A Missing Not At Random Mechanism

Censored quantile regression model can be used to measure the impact of covariates on survival time at different levels.As a complement to Cox proportional risk model,it has the advantages of easy to explain and intuitive results,and has been widely used in survival analysis.However,due to the limitations of various practical situations,the actual collected survival data may exist the coexistence of censorship and loss.A censored quantile regression model with nonignorable missing covariates is proposed for statistical analysis of such data.Specifically,firstly,the weights of missing data are allocated based on the method of inverse probability weighting,which are calculated by maximum likelihood estimation and semi-parameter estimation respectively.Then,the weights are introduced into the censored quantile regression model,and to fit the survival time.We use the traditional KM estimation to redistribute the weights of censored data,and obtained the parameter estimation of the model by the method of step-by-step iteration.At the same time,we prove the asymptotic properties of the estimates.Finally,we carried out simulations with different error distribution,censored rate,missing rate and missing covariant types.In addition,we applied the model to real tuberculosis data and analyzed the related pathogenic factors of tuberculosis.The simulation results and empirical analysis further proved the validity of the model.