Illustrating the impact of a time-varying covariate with an extended Kaplan-Meier estimator

In clinical endpoint trials, the association between a baseline covariate and the risk of an endpoint is often measured by the hazard ratio as calculated by a Cox regression model, and illustrated by Kaplan-Meier curves comparing cohorts defined by levels of the covariate. The Cox regression model is easily extended to the case of time-varying covariates; however, there is no clear approach for similarly extending the standard Kaplan-Meier estimator. Various ad hoc procedures that have been used in the medical literature are seriously flawed. This article discusses an extended Kaplan-Meier estimator that can be used with time-varying covariates and illustrates this method using data from a long-term clinical trial.