Mediation analysis is important in understanding the mechanisms of one variable causing changes in another. Measurement error could be obscuring the ability of the potential mediator to explain this mechanism. Existing correction methods in mediation analysis literature are not directly applicable to failure time data.;This dissertation focuses on developing correction methods for measurement error in the potential mediator with time-to-event outcome. We consider two specifications of measurement errors: one with technical measurement error only, and one with both technical measurement error and temporal variation. The underlying model with the true mediator values is assumed to be the Cox proportional hazards model. The hazard function induced by the observed mediator value no longer corresponds to a simple partial likelihood independent of the baseline hazard function, due to the conditioning event {T˜ ≥ t}. We propose a mean-variance regression calibration and a follow-up time calibration approach to approximate the induced partial likelihood. Both methods demonstrate successes in recovering treatment effect estimates with both types of measurement error in simulation studies. Variance estimators are derived for both approaches. These two methods can be generalized to multiple biomarkers and case-cohort design. We apply these correction methods to the Women's Health Initiative hormone therapy trials to understand the mediation effect of biomarker IGFBP4 in the relationship between hormone therapy and stroke.
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