Smoothed Weighted Quantile Regression for Censored Data in Survival Analysis

In this study, we propose a smoothed weighted quantile regression (SWQR), which combines convolution smoothing with a weighted framework to address the limitations. By smoothing the non-differentiable quantile regression loss function, SWQR can improve computational efficiency and allow for more stable model estimation in complex datasets. We construct an efficient optimization process based on gradient-based algorithms by introducing weight refinement and iterative parameter estimation methods to minimize the smoothed weighted quantile regression loss function. In the simulation studies, we compare the proposed method with two existing methods, including martingale-based quantile regression (MartingaleQR) and weighted quantile regression (WeightedQR). The results emphasize the superior computational efficiency of SWQR, outperforming other methods, particularly WeightedQR, by requiring significantly less runtime, especially in settings with large sample sizes. Additionally, SWQR maintains robust performance, achieving competitive accuracy and handling the challenges of right censoring effectively, particularly at higher quantiles. We further illustrate the proposed method using a real dataset on primary biliary cirrhosis, where it exhibits stable coefficient estimates and robust performance across quantile levels with different censoring rates. These findings highlight the potential of SWQR as a flexible and robust method for analyzing censored data in survival analysis, particularly in scenarios where computational efficiency is a key concern.