Risk scores are simple models that allow users to make quick risk predictions by adding and subtracting a few numbers. These models are widely used to predict the risk that an event will take place within a given time horizon – e.g., to predict the risk that a patient will suffer a stroke within 24 hours or will survive following a heart failure for at least 3 years. In practice, the models are designed to predict a target obtained by thresholding a time-to-event outcome, casting a survival analysis task into a classification task. In this work, we present a new method to fit risk scores for direct time-to-event prediction called TSLIM – Time-Adaptive Sparse Linear Integer Models. Our method trains models by solving a mixed-integer non-linear program that minimizes the proportional hazard loss and enforces constraints to enforce sparsity and integrality. Our approach can customize models to obey a wide range of constraints and inform the customization process by returning a certificate of optimality. We evaluate our models on real-world clinical datasets where we build time-adaptive risk scores for disease staging and compare them to standard methods for survival analysis and classification.
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