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X-CAL: Explicit Calibration for Survival Analysis
Mark Goldstein · Xintian Han · Aahlad Puli · Adler Perotte · Rajesh Ranganath

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #976

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model’s predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model’s calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows us to directly optimize calibration and strike a desired trade-off between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.

Author Information

Mark Goldstein (New York University)
Xintian Han (New York University)
Aahlad Puli (NYU)
Adler Perotte (Columbia University)
Rajesh Ranganath (New York University)

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