Countdown Regression: Sharp and Calibrated Survival Predictions
This work addresses the issue of unreliable survival predictions in healthcare, offering a method to improve sharpness and calibration for mortality prediction tasks using electronic health records.
The authors tackled the problem of high variance in probabilistic survival predictions from models trained with Maximum Likelihood Estimation by introducing Survival-CRPS, a generalization of the Continuous Ranked Probability Score for survival prediction with censored data. They showed that models trained with Survival-CRPS on EHR datasets (STARR and MIMIC-III) produced sharper predictive distributions while maintaining calibration compared to MLE-trained models.
Probabilistic survival predictions from models trained with Maximum Likelihood Estimation (MLE) can have high, and sometimes unacceptably high variance. The field of meteorology, where the paradigm of maximizing sharpness subject to calibration is popular, has addressed this problem by using scoring rules beyond MLE, such as the Continuous Ranked Probability Score (CRPS). In this paper we present the \emph{Survival-CRPS}, a generalization of the CRPS to the survival prediction setting, with right-censored and interval-censored variants. We evaluate our ideas on the mortality prediction task using two different Electronic Health Record (EHR) data sets (STARR and MIMIC-III) covering millions of patients, with suitable deep neural network architectures: a Recurrent Neural Network (RNN) for STARR and a Fully Connected Network (FCN) for MIMIC-III. We compare results between the two scoring rules while keeping the network architecture and data fixed, and show that models trained with Survival-CRPS result in sharper predictive distributions compared to those trained by MLE, while still maintaining calibration.