Censored quantile regression survival models with a cure proportion

A new quantile regression model for survival data is proposed that permits a positive proportion of subjects to become unsusceptible to recurrence of disease following treatment or based on other observable characteristics. In contrast to prior proposals for quantile regression estimation of censored survival models, we propose a new "data augmentation" approach to estimation. Our approach has computational advantages over earlier approaches proposed by Wu and Yin (2013, 2017). We compare our method with the two estimation strategies proposed by Wu and Yin and demonstrate its advantageous empirical performance in simulations. The methods are also illustrated with data from a Lung Cancer survival study.