Penalized regression across multiple quantiles under random censoring

In quantile regression, it is of interest to determine whether a covariate has varying or constant effect across quantiles, since in situations where the quantile coefficients share some common features we can improve the estimation efficiency through joint modeling of multiple quantiles. To automatically perform estimation and detection of the interquantile commonality, we propose a new penalization procedure with two variations of interquantile penalties for censored quantile regression. The proposed methods are shown to be consistent in separating the constant and varying effects across quantiles, and the resulting slope estimators have the same asymptotic efficiency with the oracle estimators obtained as if the true interquantile model structure is known a priori. Our simulation study suggests that the proposed estimators have competitive or higher efficiency than the existing estimator obtained by fitting censored quantile regression at each quintile level separately. The practical value of the proposed methods is further illustrated through the analysis of a renal disease data.