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


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We study nonparametric estimation with two types of data structures. In the first data structure we observe n i.i.d. copies of (C, N(C)) where N is a counting process and C a random monitoring time. In the second data structure we observe n i.i.d. copies of (C ^ T, I(T =< C), N(C ^ T)), 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 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. The actual nonparametric maximum likelihood estimator (NPMLE) uses all the data, but is very hard to compute. In this paper we prove that, at most data generating distributions, the ad hoc estimators yield asymptotically efficient estimators of (square root of n)-estimable parameters, and we explain why the NPMLE is more complex at these data generating distributions. The results and a simulation for a special case in van der Laan, Jewell, Peterson (1997) suggest strongly that the practical performance of the proposed simple estimators is better than the NMLE at these data generating distributions.


Statistical Methodology | Statistical Theory | Survival Analysis

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