A Nonparametric Regression Calibration for the Accelerated Failure Time Model With Measurement Error

Accelerated failure time models are appealing due to their intuitive interpretation. However, when covariates are subject to measurement errors, naive estimation becomes severely biased. To address this issue, the regression calibration (RC) approach is a widely applicable and effective method. Traditionally, the RC method requires a good predictor for the true covariate, which can be obtained through parametric distribution assumptions or validation datasets. Consequently, the performance of the estimator depends on the plausibility of these assumptions. In this work, we propose a novel method that utilizes error augmentation to duplicate covariates, facilitating nonparametric estimation. Our approach does not require a validation set or parametric distribution assumptions for the true covariate. Through simulation studies, we demonstrate that our approach is more robust and less impacted by heavy censoring rates compared to conventional analyses. Additionally, an analysis of a subset of a real dataset suggests that the conventional RC method may have a tendency to overcorrect the attenuation effect of measurement error.