Survival Analysis Under the Aalen's Additive Hazards Model With Covariate Measurement Error: Application to Causal Mediation Analysis

Covariate measurement error is an important problem in survival analysis, which has been well studied under the Cox proportional hazards model. However, measurement error effects have been rarely addressed under the Aalen's additive hazards model, and there is a lack of methods to correct for error effects. In recent years, the Aalen's additive hazards model has been increasingly used in causal mediation analysis. Although the longitudinal mediator is frequently measured with uncertainty, the issue of measurement error in the mediator has received little attention. In this article, we study the general problem of covariate measurement error under the Aalen's additive hazards model and propose a measurement error correction strategy. We then extend the proposed method to causal mediation analysis in the survival setting with an error-prone longitudinal mediator. Corrected estimation of the direct and indirect effects is obtained. The performance of the proposed method is assessed in numerical studies.