Since its emergence in late 2019, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused a pandemic with more than 55 million reported cases and 1.3 million estimated deaths worldwide. While epidemiological and clinical characteristics of COVID-19 have been reported, risk factors underlying the transition from mild to severe disease among patients remain poorly understood. In this retrospective study, we analysed data of 879 confirmed SARS-CoV-2 positive patients admitted to a two-site NHS Trust hospital in London, England, between January 1st and May 26th, 2020, with a majority of cases occurring in March and April. We extracted anonymised demographic data, physiological clinical variables and laboratory results from electronic healthcare records (EHR) and applied multivariate logistic regression, random forest and extreme gradient boosted trees. To evaluate the potential for early risk assessment, we used data available during patients’ initial presentation at the emergency department (ED) to predict deterioration to one of three clinical endpoints in the remainder of the hospital stay: admission to intensive care, need for invasive mechanical ventilation and in-hospital mortality. Based on the trained models, we extracted the most informative clinical features in determining these patient trajectories. Considering our inclusion criteria, we have identified 129 of 879 (15%) patients that required intensive care, 62 of 878 (7%) patients needing mechanical ventilation, and 193 of 619 (31%) cases of in-hospital mortality. Our models learned successfully from early clinical data and predicted clinical endpoints with high accuracy, the best model achieving area under the receiver operating characteristic (AUC-ROC) scores of 0.76 to 0.87 (F1 scores of 0.42–0.60). Younger patient age was associated with an increased risk of receiving intensive care and ventilation, but lower risk of mortality. Clinical indicators of a patient’s oxygen supply and selected laboratory results, such as blood lactate and creatinine levels, were most predictive of COVID-19 patient trajectories. Among COVID-19 patients machine learning can aid in the early identification of those with a poor prognosis, using EHR data collected during a patient’s first presentation at ED. Patient age and measures of oxygenation status during ED stay are primary indicators of poor patient outcomes.

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible "family trees," representing complex interactions between point events. We also consider the problem of computing the integrated cumulants, characterizing the average measure of correlated activity between events of different types, and derive the relevant equations.

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.