Confidence intervals for high-dimensional accelerated failure time models under measurement errors.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• High-dimensional survival analysis is crucial in fields like molecular biology and economics.
• Existing sparse modeling methods struggle with statistical inference under measurement errors.
• Valid inference in error-in-variables accelerated failure time (AFT) models is an underexplored area.

Purpose of the Study:

• To introduce a novel method, the double debiased Lasso (DDL), for robust statistical inference.
• To address challenges in high-dimensional error-in-variables AFT models.
• To construct reliable confidence intervals despite data inaccuracies.

Main Methods:

• Developed the double debiased Lasso (DDL) estimator.
• Corrected initial weighted least squares Lasso estimate bias by inverting Karush-Kuhn-Tucker (KKT) conditions.
• Mitigated measurement error impact using nearest positive semi-definite projection for estimators and inverse covariance matrices.

Main Results:

• Established asymptotic normality for the DDL estimator.
• Proved estimation consistency for the initial estimator.
• Demonstrated method effectiveness through simulations and real-world data analysis.

Conclusions:

• The DDL method provides a statistically valid approach for inference in challenging survival data.
• The technique effectively handles both high dimensionality and measurement errors.
• This work advances sparse modeling for survival data with practical implications.