Locally Efficient Estimation of the Survival Distribution with Right Censored Data and Covariates When Collection of Data is Delayed
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.
Longitudinal Data Analysis and Time Series | Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis
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.
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