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 can provide better predictive performance than regression-based approaches, not all can model time-varying interactions and complex baseline hazards. To address this, we propose Case-Base Neural Networks (CBNNs) as a new approach that combines the case-base sampling framework with flexible neural network architectures. Using a novel sampling scheme and data augmentation to naturally account for censoring, we construct a feed-forward neural network that may take time as an input. CBNNs predict the probability of an event occurring at a given moment to estimate the hazard function. We compare the performance of CBNNs to regression and neural network-based survival methods in a simulation and three case studies using two time-dependent metrics. First, we examine performance on a simulation involving a complex baseline hazard and time-varying interactions to assess all methods, with CBNN outperforming competitors. Then, we apply all methods to three real data applications, with CBNNs outperforming the competing models in two studies and showing similar performance in the third. Our results 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 single event survival outcomes. An R package is available at https://github.com/Jesse-Islam/cbnn.