  Cox proportional hazards model is one of the most popular models in
biomedical data analysis. There have been continuing efforts to improve the
flexibility of such models for complex signal detection, for example, via
additive functions. Nevertheless, the task to extend Cox additive models to
accommodate high-dimensional data is nontrivial. When estimating additive
functions, commonly used group sparse regularization may introduce excess
smoothing shrinkage on additive functions, damaging predictive performance.
Moreover, an "all-in-all-out" approach makes functional selection challenging
to answer if nonlinear effects exist. We develop an additive Cox PH model to
address these challenges in high-dimensional data analysis. Notably, we impose
a novel spike-and-slab LASSO prior that motivates the bi-level functional
selection on additive functions. A scalable and deterministic algorithm,
EM-Coordinate Descent, is designed for scalable model fitting. We compare the
predictive and computational performance against state-of-the-art models in
simulation studies and metabolomics data analysis. The proposed model is
broadly applicable to various fields of research, e.g. genomics and population
health, via the freely available R package BHAM
(https://boyiguo1.github.io/BHAM/).
