An imputation approach using subdistribution weights for deep survival analysis with competing events

With the popularity of deep neural networks (DNNs) in recent years, many researchers have proposed DNNs for the analysis of survival data (time-to-event data). These networks learn the distribution of survival times directly from the predictor variables without making strong assumptions on the underlying stochastic process. In survival analysis, it is common to observe several types of events, also called competing events. The occurrences of these competing events are usually not independent of one another and have to be incorporated in the modeling process in addition to censoring. In classical survival analysis, a popular method to incorporate competing events is the subdistribution hazard model, which is usually fitted using weighted Cox regression. In the DNN framework, only few architectures have been proposed to model the distribution of time to a specific event in a competing events situation. These architectures are characterized by a separate subnetwork/pathway per event, leading to large networks with huge amounts of parameters that may become difficult to train. In this work, we propose a novel imputation strategy for data preprocessing that incorporates weights derived from a time-discrete version of the classical subdistribution hazard model. With this, it is no longer necessary to add multiple subnetworks to the DNN to handle competing events. Our experiments on synthetic and real-world datasets show that DNNs with multiple subnetworks per event can simply be replaced by a DNN designed for a single-event analysis without loss in accuracy.