An exact corrected log-likelihood function for Cox's proportional hazards model under measurement error and some extensions

This paper studies Cox`s proportional hazards model under covariate
measurement error. Nakamura`s (1990) 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 (1992), Kong, Huang and Li (1998) and Kong and Gu (1999)
are reestablished 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.