GRAPHICAL REPRESENTATION OF SURVIVAL CURVES ASSOCIATED WITH A BINARY NON-REVERSIBLE TIME-DEPENDENT COVARIATE

The use of time dependent covariates has allowed for incorporation int o analysis of survival data intervening events that are binary and non -reversible (for example, heart transplant, initial response to chemot herapy). We can represent this type of intervening event as a three-st ate stochastic process with a starting state (S), an intervening state (I), and an absorbing state (D), which usually represents death. In t his paper we present three procedures for calculating survivorship fun ctions which attempt to display the prognostic significance of the tim e dependent covariate. The first method compares survival from baselin e for the two possible paths through the stochastic process; the secon d method compares overall survival to survival with state I removed fr om the process; and, the third method compares survival for those alre ady 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 illus trate how these methods can yield different results and in which situa tions one might employ each of the three methods. Extensions to applic ations with reversible binary time dependent covariates and models wit h both baseline and time dependent covariates are suggested.