Multiple imputation in censored quantile regression

Quantile regression is a natural extension to the traditional linear regression. Instead of modeling the conditional mean of the response variable, quantile regression models the conditional quantiles of the response. With properly selected quantiles, the quantile regression model provides a better understanding of the relationship between the response and the covariates comparing with the traditional regression models Recently this method is introduced to the area of survival analysis, where censoring is a natural characteristic of the data. To address the challenges posed by censored data, especially the specification issue at high quantiles, we propose a novel approach that employs multiple imputations of censored observations using the Buckley-James method, originally developed in the framework of classical quantile regression analysis. Our method not only ensures consistent estimators of the model parameters, but also achieves asymptotically normality when the sample size approaches infinity. Notably, it overcomes the limitations of traditional censored quantile regression, particularly in estimating extreme quantiles. Extensive simulation studies demonstrate the efficacy of our approach. Additionally, we apply our method to a Health Maintenance Organization (HMO) dataset as an illustration.