Ordinal Sparse Neural Networks for Modeling Gene- and Imaging-Environment Interactions.

In biomedical studies, gene-environment (G-E) interactions and imaging-environment (I-E) interactions play an important role in modeling disease outcomes. Substantial investigations have been made; however, there is still a lack of related studies exploring flexible nonparametric statistical methods for modeling ordinal responses, such as the tumor pathological stage. In this paper, we develop a neural network-based method for modeling ordinal responses with interaction analysis. A novel definition of the output function for the neural network is derived to predict ordinal categories. To facilitate variable selection, we employ a sparse layer within the proposed neural networks. The penalized estimation is obtained using the local quadratic approximation (LQA) algorithm. Extensive simulation studies demonstrate that the proposed method achieves competitive performance in both prediction and variable selection. We further apply our method to breast cancer (BRCA) and skin cutaneous melanoma (SKCM) datasets, examining tumor stage prediction based on G-E and I-E interaction analyses, respectively. The proposed method identifies relevant main effects and interactions, providing insights into the underlying biological mechanisms.