Corrected likelihood for proportional hazards measurement error model and its application.

Consider the case where the exact values of covariates in the proportional hazards model may not be observed but instead, only surrogates for them involving measurement errors are available. The maximum likelihood estimate based on the partial likelihood with the true covariate replaced by the observed surrogate is even asymptotically biased and may cause seriously misleading results in covariance analysis based on the partial likelihood. These facts are illustrated by Monte Carlo simulation. A correction to partial likelihood proposed by the first author is studied to gain insight into its merits and limitations in practical applications. The results indicate that when the "effective magnitude of the measurement error" as defined in this article is small, which is indeed the case for most applications, the method will be useful. Some other correction methods for the measurement error in censored survival models are also reviewed and discussed.