Semiparametric estimation for the accelerated failure time model with length-biased sampling and covariate measurement error

Analysis of survival data with biased samples caused by left-truncation or length-biased sampling has received extensive interest. Many inference methods have been developed for various survival models. These methods, however, break down when survival data are typically error contaminated. Although error-prone survival data commonly arise in practice, little work has been available in the literature for handling length-biased data with measurement error. In this paper, we study this important problem and explore valid inference methods under the accelerated failure time (AFT) model. We establish asymptotic results for the proposed estimators and examine the efficiency and robustness issues of the proposed estimators. The proposed methods enjoy appealing features in that there is no need to specify the distributions of the covariates and of the error term in the AFT model. Numerical studies are reported to assess the performance of the proposed method.