Inverse-Weighted Quantile Regression With Partially Interval-Censored Data

Abstract

This paper introduces a novel approach to estimating censored quantile regression using inverse probability of censoring weighted (IPCW) methodology, specifically tailored for data sets featuring partially interval-censored data. Such data sets, often encountered in HIV/AIDS and cancer biomedical research, may include doubly censored (DC) and partly interval-censored (PIC) endpoints. DC responses involve either left-censoring or right-censoring alongside some exact failure time observations, while PIC responses are subject to interval-censoring. Despite the existence of complex estimating techniques for interval-censored quantile regression, we propose a simple and intuitive IPCW-based method, easily implementable by assigning suitable inverse-probability weights to subjects with exact failure time observations. The resulting estimator exhibits asymptotic properties, such as uniform consistency and weak convergence, and we explore an augmented-IPCW (AIPCW) approach to enhance efficiency. In addition, our method can be adapted for multivariate partially interval-censored data. Simulation studies demonstrate the new procedure's strong finite-sample performance. We illustrate the practical application of our approach through an analysis of progression-free survival endpoints in a phase III clinical trial focusing on metastatic colorectal cancer.