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Regression calibration in semiparametric accelerated failure time models. (English) Zbl 1192.62123
Summary: In large cohort studies, it often happens that some covariates are expensive to measure and hence only measured on a validation set. On the other hand, relatively cheap but error-prone measurements of the covariates are available for all subjects. The regression calibration (RC) estimation method [R. L. Prentice, Biometrika 69, 331–342 (1982; Zbl 0523.62083)] is a popular method for analyzing such data and has been applied to the Cox model by C. Y. Wang et al. [Biometrics 53, No. 1, 131–145 (1997; Zbl 0874.62139)] under normal measurement errors and rare disease assumptions. We consider the RC estimation method for a semiparametric accelerated failure time model with covariates subject to measurement errors. Asymptotic properties of the proposed method are investigated under a two-phase sampling scheme for validation data that are selected via stratified random sampling, resulting in neither independent nor identically distributed observations. We show that the estimates converge to some well-defined parameters. In particular, unbiased estimation is feasible under additive normal measurement error models for normal covariates and under Berkson error models. The proposed method performs well in finite-sample simulation studies. We also apply the proposed method to a depression mortality study.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
92C50 Medical applications (general)
62P10 Applications of statistics to biology and medical sciences; meta analysis
62D05 Sampling theory, sample surveys
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