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 missingness