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Doubly-robust estimators of treatment-specific survival distributions in observational studies with stratified sampling. (English) Zbl 1285.62124

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 distributions 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 sub-study 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62D05 Sampling theory, sample surveys
62N02 Estimation in survival analysis and censored data
92C50 Medical applications (general)
65C60 Computational problems in statistics (MSC2010)
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