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

Area of Science:

• Biostatistics
• Medical Informatics
• Computational Biology

Background:

• High-dimensional survival data with measurement errors pose significant challenges in biomedical research.
• Accurate risk assessment is crucial but hindered by non-convex optimization problems arising from noisy covariates.

Purpose of the Study:

• To develop a robust statistical model for analyzing high-dimensional, error-prone survival data.
• To address parameter estimation and variable selection complexities in the presence of measurement errors.

Main Methods:

• Proposed an error-in-variables additive hazards regression model.
• Developed a fast Lasso approach (semi-definite projection Lasso, SPLasso) and its soft thresholding variant (SPLasso-T) using nearest positive semi-definite matrix projection.
• Established theoretical guarantees including model selection consistency and oracle inequalities.

Main Results:

• SPLasso and SPLasso-T demonstrated superior efficiency in handling high-dimensional noisy survival data.
• Methods showed remarkable performance in scenarios with missing values, indicating robustness.
• Validated through simulation studies and two real-world biomedical data applications.

Conclusions:

• The proposed error-in-variables additive hazards model and associated Lasso methods are effective for high-dimensional survival data analysis.
• These methods offer practical utility and robustness in complex biomedical settings, particularly with missing data.
• Provides a reliable framework for improved risk assessment in the presence of covariate measurement error.