  In epidemiology, identifying the effect of exposure variables in relation to
a time-to-event outcome is a classical research area of practical importance.
Incorporating propensity score in the Cox regression model, as a measure to
control for confounding, has certain advantages when outcome is rare. However,
in situations involving exposure measured with moderate to substantial error,
identifying the exposure effect using propensity score in Cox models remains a
challenging yet unresolved problem. In this paper, we propose an estimating
equation method to correct for the exposure misclassification-caused bias in
the estimation of exposure-outcome associations. We also discuss the asymptotic
properties and derive the asymptotic variances of the proposed estimators. We
conduct a simulation study to evaluate the performance of the proposed
estimators in various settings. As an illustration, we apply our method to
correct for the misclassification-caused bias in estimating the association of
PM2.5 level with lung cancer mortality using a nationwide prospective cohort,
the Nurses' Health Study (NHS). The proposed methodology can be applied using
our user-friendly R function published online.
