Variable selection for proportional hazards models with high-dimensional covariates subject to measurement error

Methods of analyzing survival data with high-dimensional covariates are often challenged by the presence of measurement error in covariates, a common issue arising from various applications. Conducting naive analysis with measurement-error effects ignored usually gives biased results. However, relatively little research has been focused on this topic. In this article, we consider this important problem and discuss variable selection for proportional hazards models with high-dimensional covariates subject to measurement error. We propose a penalized "corrected" likelihood-based method to simultaneously address the measurement-error effects and perform variable selection. We establish theoretical results including the consistency, the oracle property and the asymptotic distribution of the proposed estimator. Simulation studies are conducted to assess the finite sample performance of the proposed method. To illustrate the use of our method, we apply the proposed method to analyze a dataset arising from the breast cancer study.