Semi-Supervised Ordinal Regression via Cumulative Link Models for Predicting In-Hospital Length-of-Stay

Abstract

Length-of-stay prediction has been widely studied as a classification task: will this patient stay 0-3 days, 3-7 days, or more than 7 days? Yet previous approaches neglect the natural ordering of these classes: standard multi-class classification treats classes as unordered, while methods that build separate binary classifiers for each class struggle to enforce coherent probabilistic predictions across classes. Instead, we suggest that cumulative link models (CLMs), an ordinal approach long-known in statistics, are a naturally coherent approach well-suited to predicting length-of-stay. We describe how CLMs can be integrated as an output layer into any training pipeline based on automatic differentiation. We show that CLM output layers yield competitive predictions over binary classifier alternatives when paired with either neural net or hidden Markov model representations of patient vital sign history, all while requiring fewer parameters. Further experiments show promise in a semi-supervised setting, where only some patients have observed outcomes.