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Updated: Mar 16, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
A quantile regression model for failure-time data with time-dependent covariates
Malka Gorfine1, Yair Goldberg2, Ya'acov Ritov3
1Department of Statistics and Operation Research, Tel Aviv University, Ramat Aviv, 6997801 Tel Aviv, Israel gorfinem@post.tau.ac.il.
Abstract:
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.
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