Real-time monitoring and forecasting of time series in healthcare applications

Abstract

Type II diabetes is an increasingly common disease, but one in which the effects suffered by patients, such as hyperglycaemia, can be improved through careful monitoring and control of the factors that influence blood glucose levels. Advances in the Internet of Things (IoT) have made monitoring a person’s glucose levels more accessible, in that a continuous glucose monitoring (CGM) device in the form of a small sensor can be used to regularly report glucose levels to a bluetooth device, without the need for human intervention. Modelling the data from CGM devices online allows for short-term forecasts to be made that can assist in making real-time decisions regarding interventions to improve future glucose levels, such as behavioural changes. Additional data to monitor how active a person is can easily be collected by wrist-worn accelerometer devices. As activity levels directly impact glucose levels, bivariate models between glucose and activity data aim to provide improved forecasts. State space models are fitted to glucose data and activity data using a Bayesian modelling framework. The posterior distributions of model parameters are learned via Markov chain Monte Carlo (MCMC) methods. High frequency (100 Hz), tri-axial accelerometer data are reported alongside glucose observations recorded at five minute intervals and are transformed into univariate activity summaries. Discrete-valued state space models, known as hidden Markov models (HMMs), are used to classify the observations from the different activity summaries into activity intensities. Normal and skew Normal withinstate distributions are explored to better fit the observed activity summaries, as well as fitting models to transformations of the summaries where possible to reduce the skewness in the data. Gaussian state space models, known as dynamic linear models (DLMs), are explored to describe glucose levels, incorporating seasonal and autoregressive (AR) components. The results from these models then provide the basis for bivariate models that incorporate known activity states. This additional information is included in the DLMs as a regression covariate, which is formed by a weighted sum of lagged activity zones. Models between glucose levels and lagged carbohydrate intake are also considered, to better understand the effects of activity and food on glucose levels. A second application area is considered as an example of improved predictive performance where an influential variable is known alongside the quantity of interest. The production levels of liquid natural gas (LNG) at a gas plant are modelled by a DLM, with a regression on atmospheric temperature. The models are fitted in a frequentist framework for simplicity