Censored broken adaptive ridge rank regression via induced smoothing

Abstract

Broken adaptive ridge (BAR) penalty approximates $L_0$-regularization through iterative reweighting of L2 penalties. This penalty enjoys both the oracle property and the grouping effect for highly correlated covariates, making it particularly attractive for penalized regression with complex dependence among predictors. In this paper, we develop a BAR-penalized linear rank regression method for the semiparametric accelerated failure time model with right-censored data. Computational tractability is achieved by applying induced smoothing to the nonsmooth Gehan-type rank estimating function, yielding a more stable framework for estimation and inference. For scalable penalization, we develop a cyclic coordinate descent algorithm that minimizes the penalized objective function, and estimates the regression coefficients in a coordinate-wise manner. We further extend the proposed method to more complex survival endpoints, such as multivariate partly interval-censored (PIC) data. Under mild conditions, the proposed estimator satisfies both the oracle property and the grouping effect, and the variance estimator of the informative coefficients can be derived in analytic form. Numerical studies using synthetic data compare our approach to several well-known penalties, and demonstrate its superior selection accuracy and estimation efficiency across various scenarios. Furthermore, applications to right-censored outcomes from primary biliary cirrhosis, and correlated PIC outcomes from colorectal cancer further illustrate the practical utility of the proposed method. The R package aftPenCDA for implementing the method is available on R CRAN.