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Irregularly measured time series are common in many of the applied settingsin which time series modelling is a key statistical tool, including medicine.This provides challenges in model choice, often necessitating imputation orsimilar strategies. Continuous time autoregressive recurrent neural networks(CTRNNs) are a deep learning model that account for irregular observationsthrough incorporating continuous evolution of the hidden states betweenobservations. This is achieved using a neural ordinary differential equation(ODE) or neural flow layer. In this manuscript, we give an overview of thesemodels, including the varying architectures that have been proposed to accountfor issues such as ongoing medical interventions. Further, we demonstrate theapplication of these models to probabilistic forecasting of blood glucose in acritical care setting using electronic medical record and simulated data. Theexperiments confirm that addition of a neural ODE or neural flow layergenerally improves the performance of autoregressive recurrent neural networksin the irregular measurement setting. However, several CTRNN architecture areoutperformed by an autoregressive gradient boosted tree model (Catboost), withonly a long short-term memory (LSTM) and neural ODE based architecture(ODE-LSTM) achieving comparable performance on probabilistic forecastingmetrics such as the continuous ranked probability score (ODE-LSTM:0.118$\pm$0.001; Catboost: 0.118$\pm$0.001), ignorance score (0.152$\pm$0.008;0.149$\pm$0.002) and interval score (175$\pm$1; 176$\pm$1).

Continuous time recurrent neural networks: overview and application to forecasting blood glucose in the intensive care unit