Censored quantile regression for residual lifetimes

We propose a regression method that studies covariate effects on the conditional quantiles of residual lifetimes at a certain followup time point. This can be particularly useful in cancer studies, where more patients survive cancers initially and a patient's residual life expectancy is used to compare the efficacy of secondary or adjuvant therapies. The new method provides a consistent estimator that often exhibits smaller standard error in real and simulated examples, compared to the existing method of Jung et al. (2009). It also provides a simple empirical likelihood inference method that does not require estimating the covariance matrix of the estimator or resampling. We apply the new method to a breast cancer study (NSABP Protocol B-04, Fisher et al. (2002)) and estimate median residual lifetimes at various followup time points, adjusting for important prognostic factors.