Inverse‐Weighted Quantile Regression With Partially Interval‐Censored Data

Abstract

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.