A quantile regression model for failure-time data with time-dependent covariates

• Published in: Biostatistics (Oxford, England) Vol. 18; no. 1; pp. 132 - 146
• Main Authors: Gorfine, Malka, Goldberg, Yair, Ritov, Ya’acov
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.01.2017
• Subjects: Computer Simulation; Heart Transplantation - statistics & numerical data; Humans; Models, Statistical; Regression Analysis; Survival Analysis; Survival analysis; Instrumental variables; Quantile regression; Time-dependent covariates
• ISSN: 1465-4644; 1468-4357; 1468-4357
• DOI: 10.1093/biostatistics/kxw036

Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This article provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992, Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell, N. P., Dietz, K. and Farewell, V. T. (editors), AIDS Epidemiology. Boston: Birkhaäuser, pp. 297-331.). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset.