Cox-PASNet: Pathway-based Sparse Deep Neural Network for Survival Analysis

An in-depth understanding of complex biological processes associated to patients’ survival time at the cellular and molecular level is critical not only for developing new treatments for patients but also for accurate survival prediction. However, highly nonlinear and high-dimension, low-sample size (HDLSS) data cause computational challenges in survival analysis. We developed a novel pathway-based, sparse deep neural network, called Cox-PASNet, for survival analysis by integrating highdimensional gene expression data and clinical data. Cox-PASNet is a biologically interpretable neural network model where nodes in the network correspond to specific genes and pathways, while capturing nonlinear and hierarchical effects of biological pathways to a patient’s survival. We also provide a solution to train the deep neural network model with HDLSS data. Cox-PASNet was evaluated by comparing the performance of different cutting-edge survival methods such as Cox-nnet, SurvivalNet, and Cox elastic net (Cox-EN). Cox-PASNet significantly outperformed the benchmarking methods, and the outstanding performance was statistically assessed. We provide an open-source software implemented in PyTorch (https://github.com/DataX-JieHao/Cox-PASNet) that enables automatic training, evaluation, and interpretation of Cox-PASNet.