On interquantile smoothness of censored quantile regression with induced smoothing

Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non-smooth components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self-contradicting conclusions. We propose an estimating equation-based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap-based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite-sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and so forth.