Cure rate model with mismeasured covariates under transformation

Cure rate models explicitly account for the survival fraction in failure time data. When the covariates are measured with errors, naively treating mismeasured covariates as error-free would cause estimation bias and thus lead to incorrect inference. Under the proportional hazards cure model, we propose a corrected score approach as well as its generalization, and implement a transformation on the mismeasured covariates toward error additivity and/or normality. The corrected score equations can be easily solved through the backfitting procedure, and the biases in the parameter estimates are successfully eliminated. We show that the proposed estimators for the regression coefficients are consistent and asymptotically normal. We conduct simulation studies to examine the finite-sample properties of the new method and apply it to a real data set for illustration.