Nonstationary multivariate Gaussian processes for electronic health records

[Display omitted] •Proposing a novel non-stationary multivariate Gaussian process model for EHRs.•Providing a computationally efficient and separable version of our model.•Illustrating promising fitting and prediction performance on synthetic and real data.•Discovering a statistically significant relationship between our model and a patient health metric. Advances in the modeling and analysis of electronic health records (EHR) have the potential to improve patient risk stratification, leading to better patient outcomes. The modeling of complex temporal relations across the multiple clinical variables inherent in EHR data is largely unexplored. Existing approaches to modeling EHR data often lack the flexibility to handle time-varying correlations across multiple clinical variables, or they are too complex for clinical interpretation. Therefore, we propose a novel nonstationary multivariate Gaussian process model for EHR data to address the aforementioned drawbacks of existing methodologies. Our proposed model is able to capture time-varying scale, correlation and smoothness across multiple clinical variables. We also provide details on two inference approaches: Maximum a posteriori and Hamilton Monte Carlo. Our model is validated on synthetic data and then we demonstrate its effectiveness on EHR data from Kaiser Permanente Division of Research (KPDOR). Finally, we use the KPDOR EHR data to investigate the relationships between a clinical patient risk metric and the latent processes of our proposed model and demonstrate statistically significant correlations between these entities.