  One of the central goals in precision health is the understanding and
interpretation of high-dimensional biological data to identify genes and
markers associated with disease initiation, development, and outcomes. Though
significant effort has been committed to harness gene expression data for
multiple analyses while accounting for time-to-event modeling by including
survival times, many traditional analyses have focused separately on
non-negative matrix factorization (NMF) of the gene expression data matrix and
survival regression with Cox proportional hazards model. In this work, Cox
proportional hazards regression is integrated with NMF by imposing survival
constraints. This is accomplished by jointly optimizing the Frobenius norm and
partial log likelihood for events such as death or relapse. Simulation results
on synthetic data demonstrated the superiority of the proposed method, when
compared to other algorithms, in finding survival associated gene clusters. In
addition, using human cancer gene expression data, the proposed technique can
unravel critical clusters of cancer genes. The discovered gene clusters reflect
rich biological implications and can help identify survival-related biomarkers.
Towards the goal of precision health and cancer treatments, the proposed
algorithm can help understand and interpret high-dimensional heterogeneous
genomics data with accurate identification of survival-associated gene
clusters.

Quantitative Methods;Machine Learning;Genomics;Machine Learning