  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.
