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With increasing interest in applying machine learning to develop healthcare solutions, there is a desire to create interpretable deep learning models for survival analysis. In this paper, we extend the Neural Additive Model (NAM) by incorporating pairwise feature interaction networks and equip these models with loss functions that fit both proportional and non-proportional extensions of the Cox model. We show that within this extended framework, we can construct non-proportional hazard models, which we call TimeNAM, that significantly improve performance over the standard NAM model architecture on benchmark survival datasets. We apply these model architectures to data from the Electronic Health Record (EHR) database of Seoul National University Hospital Gangnam Center (SNUHGC) to build an interpretable neural network survival model for gastric cancer prediction. We demonstrate that on both benchmark survival analysis datasets, as well as on our gastric cancer dataset, our model architectures yield performance that matches, or surpasses, the current state-of-the-art black-box methods., Comment: Extended Abstract presented at Machine Learning for Health (ML4H) symposium 2022, November 28th, 2022, New Orleans, United States & Virtual, http://www.ml4h.cc, 14 pages