GRU-D-Weibull: A Novel Real-Time Individualized Endpoint Prediction

Accurate prediction models for individual-level endpoints and time-to-endpoints are crucial in clinical practice. In this study, we propose a novel approach, GRU-D-Weibull, which combines gated recurrent units with decay (GRU-D) to model the Weibull distribution. Our method enables real-time individualized endpoint prediction and population-level risk management. Using a cohort of 6,879 patients with stage 4 chronic kidney disease (CKD4), we evaluated the performance of GRU-D-Weibull in endpoint prediction. The C-index of GRU-D-Weibull was ~0.7 at the index date and increased to ~0.77 after 4.3 years of follow-up, similar to random survival forest. Our approach achieved an absolute L1-loss of ~1.1 years (SD 0.95) at the CKD4 index date and a minimum of ~0.45 years (SD0.3) at 4 years of follow-up, outperforming competing methods significantly. GRU-D-Weibull consistently constrained the predicted survival probability at the time of an event within a smaller and more fixed range compared to other models throughout the follow-up period. We observed significant correlations between the error in point estimates and missing proportions of input features at the index date (correlations from ~0.1 to ~0.3), which diminished within 1 year as more data became available. By post-training recalibration, we successfully aligned the predicted and observed survival probabilities across multiple prediction horizons at different time points during follow-up. Our findings demonstrate the considerable potential of GRU-D-Weibull as the next-generation architecture for endpoint risk management, capable of generating various endpoint estimates for real-time monitoring using clinical data.