#### Title

Locally Efficient Estimation of the Survival Distribution with Right Censored Data and Covariates When Collection of Data is Delayed

#### Abstract

For many sources of survival data, there is a delay between the recording of vital status and its availability to the analyst, and the Kaplan-Meier estimator is typically inconsistent in these situations. In this paper we identify the optimal estimation problem. As a result of the curse of dimensionality, no globally efficient nonparametric estimator exist with a good practical performance at moderate sample sizes. Following the approach of Robins & Rotnitzky (1992), given a correctly specified model for the hazard of censoring conditional on the delay process and T, we propose a closed form one-step estimator of the distribution of T whose asymptotic variance attains the efficiency bound, if we can correctly specify a lower dimensional working model for the conditional distribution of T given the ascertainment process. The estimator remains consistent and asymptotically normal even if this latter submodel is misspecified. In particular, if we choose as working model independence between T and the ascertainment process, then the estimator is efficient when this holds and remains consistent and asymptotically linear otherwise. Moreover, we incorporate in our data structure a covariate process that is observed during the follow-up time and is reported with the same delays. We propose closed form locally efficient estimators of the type described above which use all the data and allow for dependent censoring.

#### Disciplines

Longitudinal Data Analysis and Time Series | Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis

#### Suggested Citation

van der Laan, Mark J. and Hubbard, Alan E. , "Locally Efficient Estimation of the Survival Distribution with Right Censored Data and Covariates When Collection of Data is Delayed" (May 1997). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 65.

http://biostats.bepress.com/ucbbiostat/paper65

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## Comments

Published in Biometrika (1998), 85, 4, pp. 771-783.