Penalized Reduced Rank Regression for Multi-Outcome Survival Data Supports a Common Metabolic Risk Score for Age-Related Diseases.

The increasing availability of multi-outcome data in health research presents new opportunities for understanding complex health processes, such as aging. Aging is a multifaceted process, encompassing both lifespan and health span, as well as the onset of age-related diseases. To model this complexity, we propose the penalized reduced rank regression model for multi-outcome survival data (penalized survRRR), which identifies shared latent factors driving multiple outcomes. The model imposes a rank constraint on the coefficient matrix to capture underlying mechanisms of aging while accommodating high-dimensional and correlated predictors and outcomes by introducing penalization. We discuss the statistical properties of this doubly regularized approach and show how the optimal number of ranks can be estimated from the data. We apply a lasso-penalized reduced rank regression model to 78,553 participants of the UK Biobank, using over 200 metabolic variables as predictors and the onset of seven age-related diseases and mortality as the outcomes of interest. Our results indicate that a rank 1 model provides the best fit to the data, resulting in a single metabolite-based score of age-related disease susceptibility. This highlights the potential of the penalized survRRR model to provide new insights into the nature of the relationship between metabolomics and age-related diseases.