Quantile regression on inactivity time

• Authors: Lauren C Balmert, Northwestern University; Ruosha Li, University of Texas Health Science Center at Houston; Limin Peng, Emory University; Jong-Hyeon Jeong, University of Pittsburgh
• Journal Title: STATISTICAL METHODS IN MEDICAL RESEARCH
• Volume: Volume 30, Number 5
• Publisher: SAGE PUBLICATIONS LTD | 2021-05-01, Pages 1332-1346
• Type of Work: Article | Post-print: After Peer Review
• Publisher DOI: http://doi.org/10.1177/0962280221995977
• Subjects: Biology, Biostatistics; Health Sciences, Public Health
• Keywords: Science & Technology; Life Sciences & Biomedicine; Physical Sciences; Health Care Sciences & Services; Mathematical & Computational Biology; Medical Informatics; Statistics & Probability; Mathematics; Censoring; Donsker’ s class; lost lifespan; perturbation; time-to-event data; MEDIAN REGRESSION; SURVIVAL ANALYSIS; LIFE; INFERENCE; MODELS; TRIAL; RISKS; LOST

Abstract

The inactivity time, or lost lifespan specifically for mortality data, concerns time from occurrence of an event of interest to the current time point and has recently emerged as a new summary measure for cumulative information inherent in time-to-event data. This summary measure provides several benefits over the traditional methods, including more straightforward interpretation yet less sensitivity to heavy censoring. However, there exists no systematic modeling approach to inferring the quantile inactivity time in the literature. In this paper, we propose a semi-parametric regression method for the quantiles of the inactivity time distribution under right censoring. The consistency and asymptotic normality of the regression parameters are established. To avoid estimation of the probability density function of the inactivity time distribution under censoring, we propose a computationally efficient method for estimating the variance–covariance matrix of the regression coefficient estimates. Simulation results are presented to validate the finite sample properties of the proposed estimators and test statistics. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.