Correcting for bias due to mismeasured exposure in mediation analysis with a survival outcome

We investigate the impact of exposure measurement error on assessing mediation with a survival outcome modelled by Cox regression. We first derive the bias formulas of natural indirect and direct effects with a rare outcome and no exposure-mediator interaction. We then develop several calibration approaches to correct for the measurement error-induced bias, and generalize our methods to accommodate a common outcome and an exposure-mediator interaction. We apply the proposed methods to analyse the Health Professionals Follow-up Study (1986-2016) and evaluate the extent to which reduced body mass index mediates the protective effect of physical activity on risk of cardiovascular diseases.