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Non‐parametric Estimation of a Survival Function with Two‐stage Design Studies
Author(s) -
LI GANG,
TSENG CHIHONG
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2007.00581.x
Subject(s) - pointwise , estimator , statistics , mathematics , survival function , confidence interval , stage (stratigraphy) , sample (material) , bias of an estimator , sample size determination , kaplan–meier estimator , econometrics , survival analysis , parametric statistics , minimum variance unbiased estimator , mathematical analysis , paleontology , chemistry , chromatography , biology
. The two‐stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right‐censored survival data from a two‐stage design. A non‐parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite‐sample bias of the Kaplan–Meier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study.