Countdown Regression: Sharp and Calibrated Survival Predictions

Personalized probabilistic forecasts of time to event (such as mortality) can be crucial in decision making, especially in the clinical setting. Inspired by ideas from the meteorology literature, we approach this problem through the paradigm of maximizing sharpness of prediction distributions, subject to calibration. In regression problems, it has been shown that optimizing the continuous ranked probability score (CRPS) instead of maximum likelihood leads to sharper prediction distributions while maintaining calibration. We introduce the Survival-CRPS, a generalization of the CRPS to the time to event setting, and present right-censored and interval-censored variants. To holistically evaluate the quality of predicted distributions over time to event, we present the Survival-AUPRC evaluation metric, an analog to area under the precision-recall curve. We apply these ideas by building a recurrent neural network for mortality prediction, using an Electronic Health Record dataset covering millions of patients. We demonstrate significant benefits in models trained by the Survival-CRPS objective instead of maximum likelihood.