Improving Efficiency of Estimation and Testing for Censored Data Using Auxiliary Covariates *

Abstract

This research improves upon standard nonparametric survival estimation and testing in the two sample censored data problem. First, a survival estimator which uses prognostic covariates to more precisely get at the underlying survival curves in the presence of censoring is defined. This estimator has a smaller asymptotic variance than the usual Kaplan-Meier estimator and reduces to the Kaplan-Meier when the covariate is not prognostic or no censoring occurs. Also, this estimate remains consistent when the incorporated covariate contains information about both the censoring process and survival. Since the Kaplan-Meier is biased in this situation the author's estimate is recommended. Using this more efficient survival estimator, a more powerful test statistic for detecting differences in clinical trials is then defined. Sequential methods for using this test are also discussed. This research allows researchers to study primary endpoints rather than taking the risk of substituting a surrogate marker which may later prove useless for comparing treatments. Yet, additional information from biological markers and other important prognostic information can still be used to obtain answers more quickly and accurately.