Integrating Omics and Pathological Imaging Data for Cancer Prognosis via a Deep Neural Network‐Based Cox Model

Modeling prognosis has unique significance in cancer research. For this purpose, omics data have been routinely used. In a series of recent studies, pathological imaging data derived from biopsy have also been shown as informative. Motivated by the complementary information contained in omics and pathological imaging data, we examine integrating them under a Cox modeling framework. The two types of data have distinct properties: for omics variables, which are more actionable and demand stronger interpretability, we model their effects in a parametric way; whereas for pathological imaging features, which are not actionable and do not have lucid interpretations, we model their effects in a nonparametric way for better flexibility and prediction performance. Specifically, we adopt deep neural networks (DNNs) for nonparametric estimation, considering their advantages over regression models in accommodating nonlinearity and providing better prediction. As both omics and pathological imaging data are high-dimensional and are expected to contain noises, we propose applying penalization for selecting relevant variables and regulating estimation. Different from some existing studies, we pay unique attention to overlapping information contained in the two types of data. Numerical investigations are carefully carried out. In the analysis of TCGA data, sensible selection and superior prediction performance are observed, which demonstrates the practical utility of the proposed analysis.