Spatio-temporally Smoothed Deep Survival Neural Network

The analysis of registry data has important implications for cancer monitoring, control, and treatment. In such analysis, (semi)parametric models, such as the Cox Proportional Hazards model, have been routinely adopted. In recent years, deep neural network (DNN) has been shown to excel in many fields with its flexibility and superior prediction performance, and it has been applied to the analysis of cancer survival data. Cancer registry data usually has a broad spatial and temporal coverage, leading to significant heterogeneity. Published studies have suggested that it is not sensible to fit one model for all spatial and temporal locations combined. On the other hand, it is inefficient to fit one model for each spatial/temporal location separately. Motivated by such considerations, in this study, we develop a spatio-temporally smoothed DNN approach for the analysis of cancer registry data with a (censored) survival outcome. This approach can accommodate the significant differences across time and space, while recognizing that the spatial and temporal changes are smooth. It is effectively realized via cutting-edge optimization techniques. To draw more definitive conclusions, we also develop an approach for assessing the importance of each individual input variable. Data on head and neck cancer (HNC) and pancreatic cancer from the Surveillance, Epidemiology, and End Results (SEER) database is analyzed. Compared to direct competitors, the proposed approach leads to network architectures that are smoother. Evaluated using the time-dependent Concordance-Index, it has a better prediction performance. The important variables are also biomedically sensible. Overall, this study can deliver a new and effective tool for deciphering cancer survival at the population level.