Case-Base Neural Networks: survival analysis with time-varying, higher-order interactions

Neural network-based survival methods can model data-driven covariate interactions. While these methods have led to better predictive performance than regression-based approaches, they cannot model both time-varying interactions and complex baseline hazards. To address this, we propose Case-Base Neural Networks (CBNN) as a new approach that combines the case-base sampling framework with flexible architectures. Our method naturally accounts for censoring and does not require method specific hyperparameters. Using a novel sampling scheme and data augmentation, we incorporate time directly into a feed-forward neural network. CBNN predicts the probability of an event occurring at a given moment and estimates the hazard function. We compare the performance of CBNN to survival methods based on regression and neural networks in two simulations and two real data applications. We report two time-dependent metrics for each model. In the simulations and real data applications, CBNN provides a more consistent predictive performance across time and outperforms the competing neural network approaches. For a simple simulation with an exponential hazard model, CBNN outperforms the other neural network methods. For a complex simulation, which highlights the ability of CBNN to model both a complex baseline hazard and time-varying interactions, CBNN outperforms all competitors. The first real data application shows CBNN outperforming all neural network competitors, while a second real data application shows competitive performance. We highlight the benefit of combining case-base sampling with deep learning to provide a simple and flexible modeling framework for data-driven, time-varying interaction modeling of survival outcomes. An R package is available at https://github.com/Jesse-Islam/cbnn.