Adaptive Quantile Regression for Doubly-Censored Data

Music City Center 

Time-to-event data with a "double-censoring" structure, which includes exact observations along with left- and right-censored samples, frequently arise in biomedical and epidemiological studies. In this article, we present two efficient iterative algorithms for calculating regression quantiles in doubly-censored data settings: the Iterative Quantile Search Method (IQSM) and the Adaptive Quantile Loss via MM Algorithm (AQMM). To address this complex data structure, we develop an unbiased estimating function and the corresponding adaptive quantile loss function. This approach leverages the fact that the survival probability of the observed event time at a given quantile is a quantile-weighted average of the survival probabilities of the left- and right-censoring variables. We then reformulate the quantile loss function for doubly-censored data within the standard framework of weighted quantile regression, significantly simplifying computational requirements. The proposed estimators are shown to be consistent and asymptotically normal, ensuring robust theoretical properties. Extensive numerical studies validate the finite-sample performance of our methods, highlighting their efficiency and unbiasedness. Finally, we illustrate the practical utility of the proposed methods by analyzing the heterogeneous effects of various factors on the recovery time of COVID-19 patients.

Adaptive quantile loss

Censored quantile regression

Double-censoring

Majorization-Minimization algorithm

Survival analysis