The additive hazards model with high-dimensional regressors

Area of Science:

• Biostatistics
• Statistical Genetics
• Machine Learning in Healthcare

Background:

• High-dimensional covariate vectors, such as gene expression data, pose challenges for traditional statistical models like the Aalen additive hazards model.
• Dimension reduction techniques are essential for obtaining reliable statistical analyses in such settings.

Purpose of the Study:

• To adapt and evaluate the partial least squares (PLS) regression method for estimation and prediction within the Aalen additive hazards model framework.
• To address the challenges posed by high-dimensional covariate spaces in survival analysis.

Main Methods:

• Utilizing the Krylov sequence to naturally adapt partial least squares regression to the Aalen additive hazards model.
• Developing a PLS estimator and a standard PLS algorithm for high-dimensional survival data analysis.

Main Results:

• The proposed PLS estimator is demonstrated to be consistent under specific conditions regarding the number of included terms.
• A standard PLS algorithm yields a predictor whose relationship with original covariates is mediated by time-dependent coefficients.

Conclusions:

• Partial least squares regression, via the Krylov sequence, offers a viable approach for high-dimensional Aalen additive hazards modeling.
• The methods show practical applicability, demonstrated through analyses of breast cancer gene expression and primary biliary cirrhosis data.