  Mediation analysis is widely used in health science research to evaluate the
extent to which an intermediate variable explains an observed exposure-outcome
relationship. However, the validity of analysis can be compromised when the
exposure is measured with error. Motivated by the Health Professionals
Follow-up Study (HPFS), we investigate the impact of exposure measurement error
on assessing mediation with a survival outcome, based on the Cox proportional
hazards outcome model. When the outcome is rare and there is no
exposure-mediator interaction, we show that the uncorrected estimators of the
natural indirect and direct effects can be biased into either direction, but
the uncorrected estimator of the mediation proportion is approximately unbiased
as long as the measurement error is not large or the mediator-exposure
association is not strong. We develop ordinary regression calibration and risk
set regression calibration approaches to correct the exposure measurement
error-induced bias when estimating mediation effects and allowing for an
exposure-mediator interaction in the Cox outcome model. The proposed approaches
require a validation study to characterize the measurement error process. We
apply the proposed approaches to the HPFS (1986-2016) to evaluate extent to
which reduced body mass index mediates the protective effect of vigorous
physical activity on the risk of cardiovascular diseases, and compare the
finite-sample properties of the proposed estimators via simulations.
