Continuous, automated surveillance systems that incorporate machine learning models are becoming increasingly common in healthcare environments. These models can capture temporally dependent changes across multiple patient variables and can enhance a clinician's situational awareness by providing an early warning alarm of an impending adverse event such as sepsis. However, most commonly used methods, e.g., XGBoost, fail to provide an interpretable mechanism for understanding why a model produced a sepsis alarm at a given time. The ``black box'' nature of many models is a severe limitation as it prevents clinicians from independently corroborating those physiologic features that have contributed to the sepsis alarm. To overcome this limitation, we propose a generalized linear model (GLM) approach to fit a Granger causal graph based on the physiology of several major sepsis-associated derangements (SADs). We adopt a recently developed stochastic monotone variational inequality (VI)-based estimator coupled with forwarding feature selection to learn the graph structure from both continuous and discrete-valued as well as regularly and irregularly sampled time series. Theoretically, we develop a non-asymptotic upper bound on the estimation error for any monotone link function in the GLM. Using synthetic and real-data examples, we demonstrate that the proposed method enjoys result interpretability while achieving comparable performance to popular methods such as XGBoost.
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