Current Status and Right-Censored Data Structures When Observing a Marker at the Censoring Time

Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

We study nonparametric estimation with two types of data structures. In the first data structure n i.i.d. copies of (C,N (C) ) are observed, where N is a counting process jumping at time variables of interest and C a random monitoring time. In the second data structure n i.i.d. copies of (C ^ T, I(T =< C), N (C ^ T)) are observed, where N is a counting process with a final jump at time T (e.g., death). This data structure includes observing right-censored data on T and a marker variable at the censoring time.

In these data structures, easy to compute estimators, namely (Weighted)-Pool-Adjacent-Violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan-Meier estimator for the time T until the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that, at most continuous data generating distributions with compact support, the ad hoc estimators yield asymptotically efficient estimators of (square root of n)-estimable parameters.