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.

Discrimination, calibration, and point estimate accuracy of GRU-D-Weibull architecture for real-time individualized endpoint prediction

Real-time individual endpoint prediction has always been a challenging task but of great clinic utility for both patients and healthcare providers. With 6,879 chronic kidney disease stage 4 (CKD4) patients as a use case, we explored the feasibility and performance of gated recurrent units with decay that models Weibull probability density function (GRU-D-Weibull) as a semi-parametric longitudinal model for real-time individual endpoint prediction. GRU-D-Weibull has a maximum C-index of 0.77 at 4.3 years of follow-up, compared to 0.68 achieved by competing models. The L1-loss of GRU-D-Weibull is ~66% of XGB(AFT), ~60% of MTLR, and ~30% of AFT model at CKD4 index date. The average absolute L1-loss of GRU-D-Weibull is around one year, with a minimum of 40% Parkes serious error after index date. GRU-D-Weibull is not calibrated and significantly underestimates true survival probability. Feature importance tests indicate blood pressure becomes increasingly important during follow-up, while eGFR and blood albumin are less important. Most continuous features have non-linear/parabola impact on predicted survival time, and the results are generally consistent with existing knowledge. GRU-D-Weibull as a semi-parametric temporal model shows advantages in built-in parameterization of missing, native support for asynchronously arrived measurement, capability of output both probability and point estimates at arbitrary time point for arbitrary prediction horizon, improved discrimination and point estimate accuracy after incorporating newly arrived data. Further research on its performance with more comprehensive input features, in-process or post-process calibration are warranted to benefit CKD4 or alike terminally-ill patients.