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Doubly‐Robust Estimators of Treatment‐Specific Survival Distributions in Observational Studies with Stratified Sampling
Author(s) -
Bai Xiaofei,
Tsiatis Anastasios A.,
O'Brien Sean M.
Publication year - 2013
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12076
Subject(s) - confounding , covariate , estimator , statistics , observational study , econometrics , mathematics , robustness (evolution) , stratified sampling , survival analysis , biology , biochemistry , gene
Summary Observational studies are frequently conducted to compare the effects of two treatments on survival. For such studies we must be concerned about confounding; that is, there are covariates that affect both the treatment assignment and the survival distribution. With confounding the usual treatment‐specific Kaplan–Meier estimator might be a biased estimator of the underlying treatment‐specific survival distribution. This article has two aims. In the first aim we use semiparametric theory to derive a doubly robust estimator of the treatment‐specific survival distribution in cases where it is believed that all the potential confounders are captured. In cases where not all potential confounders have been captured one may conduct a substudy using a stratified sampling scheme to capture additional covariates that may account for confounding. The second aim is to derive a doubly‐robust estimator for the treatment‐specific survival distributions and its variance estimator with such a stratified sampling scheme. Simulation studies are conducted to show consistency and double robustness. These estimators are then applied to the data from the ASCERT study that motivated this research.