Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors.

Area of Science:

• Biostatistics
• Survival Analysis
• High-Dimensional Data Analysis

Background:

• High-dimensional survival data analysis is crucial but challenged by covariate measurement errors.
• Existing methods often struggle to adequately correct for these biases, leading to inaccurate inferences.
• Additive hazards models are widely used but require robust estimation in the presence of errors.

Purpose of the Study:

• To develop a robust inferential procedure for additive hazards regression in high-dimensional settings with measurement errors.
• To propose a double bias correction method that addresses errors from both measurement inaccuracies and regularization techniques.
• To provide a statistically sound and computationally feasible approach for analyzing complex survival data.

Main Methods:

• A double bias correction strategy is employed, first addressing measurement error bias using an estimating function.
• Convex relaxation and regularization techniques are utilized to obtain a regularized estimator, solved via linear programming.
• Neyman orthogonality is applied to derive an asymptotically unbiased estimator, correcting for regularization-induced bias.

Main Results:

• The proposed method yields a regularized estimator with a derived convergence rate.
• Asymptotic normality is established for low-dimensional parameter estimators and their linear combinations.
• A consistent variance estimator is provided, validating the theoretical framework.

Conclusions:

• The double bias correction method effectively handles measurement errors and regularization bias in high-dimensional survival data.
• Numerical experiments on simulated and real datasets confirm the method's superior performance.
• This approach offers a significant advancement for accurate statistical inference in complex survival data analysis.