Semiparametric methods for survival data with measurement error under additive hazards cure rate models

It is well established that measurement error has drastically negative impact on data analysis. It can not only bias parameter estimates but may also cause loss of power for testing relationship between variables. Although survival analysis of error-contaminated data has attracted extensive interest, relatively little attention has been paid to dealing with survival data with error-contaminated covariates when the underlying population is characterized by a cured fraction. In this paper, we consider this problem for which lifetimes of the non-cured individuals are featured by the additive hazards model and the measurement error process is described by an additive model. Unlike estimating the relative risk in the proportional hazards model, the additive hazards model allows us to estimate the absolute risk difference associated with the covariates. To allow the model flexibility, we incorporate time-dependent covariates in the model. We develop estimation methods for the two scenarios, without or with measurement error. The proposed methods are evaluated from both the theoretical view point and the numerical perspectives. Furthermore, a real-life data application is presented to illustrate the utility of the methodology.