Explain Variance of Prediction in Variational Time Series Models for Clinical Deterioration Prediction

TL;DR

This work addresses explainability of predictive uncertainty in clinical deterioration by introducing variance SHAP for variational time series models. It constructs a deterministic variance game using posterior hidden states and applies Delta's method to attribute prediction variance to input features, enabling actionable insights about measurement frequency. Experiments on MIMIC-IV ICU data reveal that longer intervals between measurements generally increase prediction variance, though some variables (notably blood pressure) show abnormal patterns due to baseline population values. The approach offers a pathway to optimize measurement schedules and improve interpretability, while noting limitations and avenues for future clinical validation and refinement.

Abstract

Missingness and measurement frequency are two sides of the same coin. How frequent should we measure clinical variables and conduct laboratory tests? It depends on many factors such as the stability of patient conditions, diagnostic process, treatment plan and measurement costs. The utility of measurements varies disease by disease, patient by patient. In this study we propose a novel view of clinical variable measurement frequency from a predictive modeling perspective, namely the measurements of clinical variables reduce uncertainty in model predictions. To achieve this goal, we propose variance SHAP with variational time series models, an application of Shapley Additive Expanation(SHAP) algorithm to attribute epistemic prediction uncertainty. The prediction variance is estimated by sampling the conditional hidden space in variational models and can be approximated deterministically by delta's method. This approach works with variational time series models such as variational recurrent neural networks and variational transformers. Since SHAP values are additive, the variance SHAP of binary data imputation masks can be directly interpreted as the contribution to prediction variance by measurements. We tested our ideas on a public ICU dataset with deterioration prediction task and study the relation between variance SHAP and measurement time intervals.

Figures (11)

• Figure 1: Proposed architecture for explaining prediction variance. Contributions in blue. The prediction variance can be deterministically approximated from the posterior distribution of hidden states via Delta's method, which is essentially a Taylor expansion.
• Figure 2: Variational Recurrent Models
• Figure 3: Patient Deterioration Prediction TaskLiu2022-nbharutyunyan2019multitask
• Figure 4: Prediction SHAP value.
• Figure 5: Variance of the prediction SHAP value