  In the context of survival analysis, data-driven neural network-based methods
have been developed to model complex covariate effects. While these methods may
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 includes
time as an input. CBNNs predict the probability of an event occurring at a
given moment to estimate the full 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
framework for data-driven modeling of single event survival outcomes that
estimates time-varying effects and a complex baseline hazard by design. An R
package is available at https://github.com/Jesse-Islam/cbnn.
