abstract
- This research integrates deep learning, copula functions, and survival analysis to effectively handle highly correlated and right-censored multivariate survival data. It introduces copula-based activation functions (Clayton, Gumbel, and their combinations) to model the nonlinear dependencies inherent in such data. Through simulation studies and analysis of real breast cancer data, our proposed CNN-LSTM with copula-based activation functions for multivariate multi-types of survival responses enhances prediction accuracy by explicitly addressing right-censored data and capturing complex patterns. The model¿s performance is evaluated using Shewhart control charts, focusing on the average run length (ARL). © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.