SPLasso for high-dimensional additive hazards regression with covariate measurement error.

High-dimensional error-prone survival data are prevalent in biomedical studies, where numerous clinical or genetic variables are collected for risk assessment. The presence of measurement errors in covariates complicates parameter estimation and variable selection, leading to non-convex optimization challenges. We propose an error-in-variables additive hazards regression model for high-dimensional noisy survival data. By employing the nearest positive semi-definite matrix projection, we develop a fast Lasso approach (semi-definite projection Lasso, SPLasso) and its soft thresholding variant (SPLasso-T), both with theoretical guarantees. Under mild assumptions, we establish model selection consistency, oracle inequalities, and limiting distributions for these methods. Simulation studies and two real data applications demonstrate the methods' superior efficiency in handling high-dimensional data, particularly showcasing remarkable performance in scenarios with missing values, highlighting their robustness and practical utility in complex biomedical settings.