Graphical representation of survival curves associated with a binary non‐reversible time dependent covariate
Citations Over Time
Abstract
The use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non-reversible (for example, heart transplant, initial response to chemotherapy). We can represent this type of intervening event as a three-state stochastic process with a starting state (S), an intervening state (I), and an absorbing state (D), which usually represents death. In this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate. The first method compares survival from baseline for the two possible paths through the stochastic process; the second method compares overall survival to survival with state I removed from the process; and, the third method compares survival for those already in state I at a landmark time x to those in state S at time x who will never enter state I. We develop discrete hazard estimates for the survival curves associated with the three methods. Two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods. Extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested.
Related Papers
- → TIME-DEPENDENT COVARIATES IN THE COX PROPORTIONAL-HAZARDS REGRESSION MODEL(1999)1,040 cited
- → Reduced-rank hazard regression for modelling non-proportional hazards(2005)36 cited
- → pcoxtime: Penalized Cox Proportional Hazard Model for Time-dependent Covariates(2021)2 cited
- The semiparametric mixture models for the analysis of survival data of long-term survivors(2009)
- → Outlier and Time-Dependent Covariate in Survival Analysis, A Simulation Based Study(2023)