Regression Analysis for the Additive Hazards Model with Covariate Errors

Abstract

In this article, general inference procedures are proposed for the additive hazards model when covariates are subject to measurement errors and the errors are non-informative. The methods are not restricted to classical additive error models, but are capable of handling general covariate error structures. They can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The asymptotic properties of the resulting estimators are derived, and simulation studies are conducted to evaluate the performance of the proposed estimators. A real example is provided.

Keywords:

• Additive hazards model
• Censoring
• Errors in variables
• Failure time
• Surrogate covariate

Mathematics Subject Classification:

• Primary 62N02
• Secondary 62G20

Acknowledgments

The first author's research was partly supported by the National Natural Science Foundation of China Grants (Nos. 10731010, 10971015 and 10721101), the National Basic Research Program of China (973 Program) (No. 2007CB814902) and Key Laboratory of RCSDS, CAS (No. 2008DP173182). The second author's research was fully supported by a grant (450508) from the Research Grant Council of the Hong Kong Special Administration Region.

Notes

PS stands for the proposed estimator when p(x | z) is known, PSV stands for the proposed estimator when p(x | z) is unknown, CS stands for the corrected pseudoscore estimator with known error parameters, CSV stands for the corrected pseudoscore estimator with unknown error parameters, UP stands for the updated pseudoscore estimator, full stands for the full data estimator, and NV stands for the naive estimator.

PS stands for the proposed estimator when p(x | z) is known, PSV stands for the proposed estimator when p(x | z) is unknown, CS stands for the corrected pseudoscore estimator with known error parameters, CSV stands for the corrected pseudoscore estimator with unknown error parameters, full stands for the full data estimator, and NV stands for the naive estimator.

PS stands for the proposed estimator when p(x | z) is known, PSV stands for the proposed estimator when p(x | z) is unknown, full stands for the full data estimator, and NV stands for the naive estimator.

PS stands for the proposed estimator when p(x | z) is known, PSV stands for the proposed estimator when p(x | z) is unknown, full stands for the full data estimator, and NV stands for the naive estimator.

PS stands for the proposed estimator when p(x | z) is known, PSVM stands for the proposed estimator when p(x | z) is unknown and is misspecified, full stands for the full data estimator, and NV stands for the naive estimator.

PSV stands for the proposed estimator when p(x | z) is unknown, PS stands for the proposed estimator when p(x | z) is known, and NV stands for the naive estimator