Cox

Cox implements a group-sparse lasso solver for multi-response Cox proportional hazards models to improve prediction in high-dimensional survival data with few uncensored events by leveraging shared predictors across related outcomes; this implementation corresponds to Multi-snpnet-Cox (mrcox).

Key Features:

• Sparse-Group Regularization: Employs sparse-group (group-sparse lasso) regularization within the Cox regression framework to borrow strength across predictors and responses for rare-event survival outcomes.
• Multi-Response Analysis: Integrates multiple related survival responses to jointly estimate effects and exploit shared predictor sets across diseases or outcomes.
• Optimization Algorithm: Uses an accelerated proximal gradient optimization algorithm to enable scalable estimation on large genomic datasets.
• Screening Procedure: Incorporates a variable screening procedure inspired by Qian et al. to reduce the set of candidate predictors prior to model fitting.

Scientific Applications:

• Genomics: Joint modeling of multiple disease survival outcomes to improve discovery and prediction of genetic markers associated with time-to-event phenotypes.
• Epidemiology: Analysis of high-dimensional covariates in cohort studies with few uncensored events to estimate hazard relationships across related endpoints.
• Biobank-scale survival analysis: Application to large datasets such as UK Biobank where many common and less prevalent diseases are recorded for the same individuals.

Methodology:

Applies sparse-group regularization within the Cox proportional hazards model for simultaneous multi-response analysis, solved using an accelerated proximal gradient optimizer and a screening procedure inspired by Qian et al.