Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes

Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Clinically relevant and interpretable results require a framework that can (1) infer temporal interactions across multiple patient features found in EMR data (e.g., labs, vital signs, etc.) and (2) can identify patterns that precede and are specific to an impending adverse event (e.g., sepsis). In this work, we propose a linear multivariate Hawkes process model, coupled with ReLU link function, to recover a Granger Causal (GC) graph with both exciting and inhibiting effects. We develop a scalable two-phase gradient-based method to maximize a surrogate-likelihood and estimate the problem parameters, which is shown to be effective via extensive numerical simulation. Our method is subsequently extended to a data set of patients admitted to an academic level 1 trauma center located in Atalanta, GA, where the estimated GC graph identifies several highly interpretable chains that precede sepsis. Here, we demonstrate the effectiveness of our approach in learning a Granger causal graph over Sepsis Associated Derangements (SADs), but it can be generalized to other applications with similar requirements.