A Hierarchical Approach to Multi-Event Survival Analysis

Abstract In multi-event survival analysis, one aims to predict the probability of multiple different events occurring over some time horizon. One typically assumes that the timing of events is drawn from some distribution conditioned on an individual's covariates. However, during training, one does not have access to this distribution, and the natural variation in the observed event times makes the task of survival prediction challenging, on top of the potential interdependence among events. To address this issue, we introduce a novel approach for multi-event survival analysis that models the probability of event occurrence hierarchically at different time scales, using coarse predictions (e.g., monthly predictions) to iteratively guide predictions at finer and finer grained time scales (e.g., daily predictions). We evaluate the proposed approach across several publicly available datasets in terms of both intra-event, inter-individual (global) and intra-individual, inter-event (local) consistency. We show that the proposed method consistently outperforms well-accepted and commonly used approaches to multi-event survival analysis. When estimating survival curves for Alzheimer's disease and mortality, our approach achieves a C-index of 0.91 (95% CI 0.88-0.93) and a local consistency score of 0.97 (95% CI 0.94-0.98) compared to a C-index of 0.75 (95% CI 0.70-0.80) and a local consistency score of 0.94 (95% CI 0.91-0.97) when modeling each event separately. Overall, our approach improves the accuracy of survival predictions by iteratively reducing the original task to a set of nested, simpler subtasks.