Nonparametric survival estimation using prognostic longitudinal covariates

One of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right-censored data. This research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual. We begin by defining a survival estimate which uses time-dependent covariates to more precisely get at the underlying survival curves in the presence of censoring. This estimate has a smaller asymptotic variance than the usual Kaplan-Meier in the presence of censoring and reduces to the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) in situations where the covariate is not prognostic or no censoring occurs. In addition, this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information. Because the Kaplan-Meier estimate is known to be biased in this situation due to informative censoring, we recommend use of our estimate.