Abstract
The proportional hazards (PH) regression model is commonly used to characterize the relationship between some time-to-event and covariates. Covariates values are frequently subject to measurement error. Substituting mismeasured values for the true covariates in the PH model leads to biased estimation. (1998) have proposed to base estimation for the PH model with covariate measurement error on a joint likelihood for survival and the covariate. The authors have used nonparametric maximum likelihood estimation (NPMLE) and have conducted simulations to assess the asymptotic validity of this approach. In this paper, we derive rigorous proofs of existence and consistency of the NPML estimators.
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