Granger Causal Chain Discovery for Sepsis-Associated Derangements via Multivariate 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 clearly elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Currently there does not exist a reliable framework for discovering or describing causal chains that precede adverse hospital events. 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 pattern(s) which 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 $g(x) = x^+$ link function to allow potential inhibition effects, in order to recover a Granger Causal (GC) graph. We develop a two-phase gradient-based scheme to maximize a surrogate of likelihood to estimate the problem parameters. This two-phase algorithm is scalable and shown to be effective via our numerical simulation. It is subsequently extended to a data set of patients admitted to Grady hospital system in Atalanta, GA, where the fitted Granger Causal graph identifies several highly interpretable chains that precede sepsis.