Deep State-Space Generative Model For Correlated Time-to-Event Predictions

TL;DR

This paper presents a deep latent state-space generative model for correlated time-to-event predictions from EMR time-series. It models latent patient states that evolve under intrinsic dynamics and interventions, with event hazards for multiple outcomes given by $\lambda^e_t = \mathcal{L}^e(\mathbf{z}_t)$ and survival tracked via $S^e(t) = \prod_{s=1}^t (1-\lambda^e_s)$. The approach is learned via variational inference using an ELBO that couples time-to-event likelihood with a KL regularization term, enabling joint prediction of mortality and organ failures. Experiments on the MIMIC-III dataset show that the method outperforms state-of-the-art baselines and yields interpretable hazard trajectories and cross-event correlations that can support clinical decision-making.

Abstract

Capturing the inter-dependencies among multiple types of clinically-critical events is critical not only to accurate future event prediction, but also to better treatment planning. In this work, we propose a deep latent state-space generative model to capture the interactions among different types of correlated clinical events (e.g., kidney failure, mortality) by explicitly modeling the temporal dynamics of patients' latent states. Based on these learned patient states, we further develop a new general discrete-time formulation of the hazard rate function to estimate the survival distribution of patients with significantly improved accuracy. Extensive evaluations over real EMR data show that our proposed model compares favorably to various state-of-the-art baselines. Furthermore, our method also uncovers meaningful insights about the latent correlations among mortality and different types of organ failures.

Figures (6)

• Figure 1: Time-calibrated multiple event risk trajectory. Given the past blood pressure readings (red dots) and Dopamine dosage (green square) in the upper left, the model captures how the risk of different types of clinical outcomes (mortality, neural system failure, etc.) can change with time in the future at the bottom right.
• Figure 2: Graphical Model of State-based Hazard Rate.
• Figure 3: Graphical Model of Multi-Event-Type Hazard Rate.
• Figure 4: Loss Computation Process. The state-space computation task (leftmost) captures the changing dynamics of patients' latent states $\mathbf{z}_{1:t}$ based on past observations and interventions. Each following task of event prediction (mortality, kidney failure, etc.) has it own survival and density function that depend on these latent states $\mathbf{z}_{1:t}$.
• Figure 5: Event hazard rate and true occurrence time for both observed (in solid dot) and censored (in light cross) events. For each prediction task, the fitted hazard rate is able to capture the true event time accurately, while for the censored events, the respective hazard rates are low as expected.