Displaying survival of patient groups defined by covariate paths: Extensions of the Kaplan-Meier estimator

Extensions of the Kaplan-Meier estimator have been developed to illustrate the relationship between a time-varying covariate of interest and survival. In particular, Snapinn et al and Xu et al developed estimators to display survival for patients who always have a certain value of a time-varying covariate. These estimators properly handle time-varying covariates, but their clinical interpretation is limited. It is of greater clinical interest to display survival for patients whose covariates lie along certain defined paths. In this article, we propose extensions of Snapinn et al and Xu et al's estimators, providing crude and covariate-adjusted estimates of the survival function for patients defined by covariate paths. We also derive analytical variance estimators. We demonstrate the utility of these estimators with medical examples and a simulation study.