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- Title
An Exact Corrected Log-Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions.
- Authors
Augustin, Thomas
- Abstract
This paper studies Cox's proportional hazards model under covariate measurement error. Nakamura's [ Biometrika 77 (1990) 127] methodology of corrected log-likelihood will be applied to the so-called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non-normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura [Biometrics 48 (1992) 829], Kong et al. [ Scand. J. Statist. 25 (1998) 573] and Kong & Gu [ Statistica Sinica 9 (1999) 953] are re-established in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.
- Subjects
ANALYSIS of covariance; ERROR analysis in mathematics; MATHEMATICS; STATISTICS; ESTIMATION theory; REGRESSION analysis
- Publication
Scandinavian Journal of Statistics, 2004, Vol 31, Issue 1, p43
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2004.00371.x