ABSTRACT
This chapter reviews quantile regression methods with randomly censored data. It outlines the extensions of Peng and Y. Huang's methods for left censored or truncated survival data and for survival data with a cure fraction Ji et al.; Wu and Yin. Quantile regression has natural appeals in model flexibility and interpretability. It has received increased attention in survival analysis because event times themselves are often of scientific interest, and quantiles are more flexible and robust quantitative tools for characterizing event times than mean-based devices. In addition, quantile regression permits investigating particular local features of the conditional distribution of an event time of interest. Wang and Wang proposed an adaptation of Zhou's method for quantile regression analysis of length-biased survival data. In the presence of a substantial fraction of long-term survivors who are either cured or immune to the event of interest, the survival times tend to be highly right-skewed.
