2 This work suggests two methods-both relying on stacked regression and data fusion of CGM and activity-to predict the blood glucose level of patients with type 1 diabetes. Method 1 uses histories of CGM data appended with the average of activity data in the same histories to train three base regressions: a multilayer perceptron, a long short- term memory, and a partial least squares regression. In Method 2, histories of CGM and activity data are used separately to train the same base regressions. In both methods, the predictions from the base regressions are used as features to create a combined model. This model is then used to make the final predictions. The results obtained show the effectiveness of both methods. Method 1 provides slightly better results.
The literature emphasises the importance of the management of type
1 diabetes mellitus (T1DM) in reducing complications associated
with the disease [
The prediction of BGL from current and past information can be
a useful contributor [
BGL prediction models could be classified into three main
groups: physiological models, data-driven models, and hybrid
models. Data-driven models explain the relationship between the
present and past information to BGL prediction. In this regard,
machine learning and time series approaches have been widely used
[
Many studies have proposed data-driven BGL prediction methodologies. Mirshekarian et al. [8], Bertachi et al. [9], Martinsson et al. [10], Zhu et al. [11] and Xie et al. [12] in separate studies, developed prediction models to forecast BGL with a prediction horizon of up to 60 minutes.
Mirshekarian’s model was based on a recursive neural network (RNN), which utilised long short- term memory (LSTM) units. CGM, insulin, meal, and activity information were inputs of their model. Bertachi used physiological models of insulin, carbohydrate, and activity on board to train an artificial neural network (ANN). Martinsson proposed an RNN model trained on historical blood glucose information to predict BGL in two horizons of 30 and 60 minutes. Zhu generated a dilated deep convolutional neural network fed by CGM, insulin, and carbohydrate intake as inputs. Xie applied an autoregression with exogenous inputs approach to predict BGL by exploiting current and past information of CGM data.
Physical activity is a critical factor in diabetes management. Therefore, investigation of the activity data in BGL prediction models is encouraged [13]. However, developing models with high accuracy using activity and CGM data is challenging, and limited studies have been done in this area. Data fusion of activity and CGM data normally result in models with a performance not comparable with those using CGM alone.
This paper proposes two novel CGM and activity data fusion methods to generate BGL prediction models with performance comparable with those using CGM data alone. 2
To develop BGL prediction algorithms, we used the OhioT1DM dataset [14]. The dataset contains eight weeks’ worth data of 12 people with T1DM. The data of six patients was released in 2018 for the first BGL prediction challenge [15] and data for additional six patients (referred by ID 540, 544, 552, 567, 584, and 596) was released for the second BGL prediction challenge in 2020 [14]. In this work, we used the data of the latter six patients.
The dataset includes data of CGM sensor, physical activity band, physiological sensor, and self-reported life-event. Among the different collected data, we explored CGM and activity data which were collected every 5 and 1 minutes, respectively. Detailed information about the sensors and devices as well as characteristics of the patients has been published [14], [15].
In the dataset, there are three types of activity data consisting of galvanic skin response, skin temperature, and magnitude of acceleration. In this work, we only used the data of the magnitude of acceleration. Hereafter, for simplicity, ‘magnitude of acceleration’ is referred to as ‘activity’. 3
This section presents the information about data preprocessing and the methodologies developed for the prediction of BGL. hidden layers used ReLU as the activation function. Mean squared error was the loss function, Adam was the optimiser. The model trained with 100 epochs with a learning rate of 0.01.
PLSR carries considerable popularity in different applications, such as glucose sensing [18]. In this work, PLSR was applied as a regression tool. Different values were considered for the number of components—ranging from one to the length of the input window. Each time, the predicted residual sum of squares ( ) was calculated as follows.
=1 = ∑( − ̂ )2 (1) value, and ̂ is the predicted value.
Where, N is the size of the evaluation set, and is the reference The number of components ( ) resulting in the minimum value /( − − 1) is then selected [19].
Stacked regression is applied to enhance the performance of BGL prediction [20]. This technique uses predictions from a number of models—first-level models—as features to train a new model— second-level model. In this work, a stacked regression structure was employed where the three base regressions mentioned in 2.3.1 were set as its first-level models and a PLSR as the second-level model (Figure 1). 3.1
Missing data in the training set is imputed using linear interpolation. For the testing set, on the other hand, linear extrapolation is used. This is to assure that future data is not seen by the model, and that the model can be used for a real-time application. Thus, we convert CGM and activity data to regular time series without any missing data in 5-minute and 1-minute intervals, respectively.
The next step was to unify the resolution of CGM and activity data. To do so, we downsampled the activity time series data to 5minute intervals by capturing the nearest activity data to each CGM data and discarding the rest.
There were a considerable number of unavailable activity data at the beginning and/or end of training and/or test set. This was due to the difference in wear time of CGM and activity sensors. For these points average of activity data in the training set is used rather than linear interpolation or extrapolation. Table 1 shows the number of unavailable activity data for each patient ID. fully-connected layer with 100 nodes and an output layer. Both horizon, two histories of 30 and 60 minutes were tried for training producing six first-level models rather than three. [14]. To train and evaluation purposes, we used the training and
, ̂ , and N have the same meaning as in (1). 4
In this section, the results of RMSE and MAE for prediction testing sets, respectively. Extrapolated data and, the first 60 minutes models are provided for both prediction horizons of 30 and 60 of the test set was excluded when calculating the evaluation metrics. minutes.
Models with a performance dependent on random The latter is because the testing set starts immediately after the initialisation ran five times, and the mean and standard deviation of training set, and they are chronologically close to each other. results are reported. We have used the acronym PH for the prediction Summarised statistics of the testing set for each patient is given in horizon in the tables. | − ̂ |
PH: 30 min
PH: 60 min
RMSE 21.19 ± 0.07 17.40 ± 0.08 16.25 ± 0.07 20.40 ± 0.07 21.54 ± 0.06 17.17 ± 0.10
This work contributes to the prediction of BGL by proposing two methodologies for data fusion of CGM and activity using stacked regression.
In the first method, the average value of activity data added to a window of CGM data was used as input to train prediction models. Initially, three base regression models consist of MLP, LSTM, and PLSR were trained. Subsequently, predictions from these base models were used as features to train a new PLSR model which then made final predictions.
In the second method, the same base regressions were trained once using windows of activity data and once using CGM data. The predictions of all trained base models were then fed as features to a new PLSR model for its training process. The new PLSR was used to make refined predictions.
The results obtained show that Method 1 (average value of activity data added to the window of CGM data) had a slightly better performance than Method 2 (first-level models trained twice, once with a history of CGM data, once using a history of activity data). In overall, Method 1 using a history of 30 minutes had the best results by providing a RMSE of 18.99 and 33.39 for the prediction horizon of 30 minutes and 60 minutes, respectively. 6
To implement the models, we used Python 3.6, TensorFlow 1.15.0 and Keras 2.2.5. Also, Pandas, NumPy and Sklearn packages of python were used. The codes were run on a commodity laptop. The codes of our implementation are available at: https://gitlab.com/Hoda-Nemat/data-fusionstacking.git