Neural-network transformation models for counting processes

While many survival models have been invented, the Cox model and the proportional odds model are among the most popular ones. Both models are special cases of the linear transformation model. The linear transformation model typically assumes a linear function on covariates, which may not reflect the complex relationship between covariates and survival outcomes. Nonlinear functional form can also be specified in the linear transformation model. Nonetheless, the underlying functional form is unknown and mis-specifying it leads to biased estimates and reduced prediction accuracy of the model. To address this issue, we develop a neural-network transformation model. Similar to neural networks, the neural-network transformation model uses its hierarchical structure to learn complex features from simpler ones and is capable of approximating the underlying functional form of covariates. It also inherits advantages from the linear transformation model, making it applicable to both time-to-event analyses and recurrent event analyses. Simulations demonstrate that the neural-network transformation model outperforms the linear transformation model in terms of estimation and prediction accuracy when the covariate effects are nonlinear. The advantage of the new model over the linear transformation model is also illustrated via two real applications.