Mixed-effects neural network modelling to predict longitudinal trends in fasting plasma glucose

Accurate fasting plasma glucose (FPG) trend prediction is important for management and treatment of patients with type 2 diabetes mellitus (T2DM), a globally prevalent chronic disease. (Generalised) linear mixed-effects (LME) models and machine learning (ML) are commonly used to analyse longitudinal data; however, the former is insufficient for dealing with complex, nonlinear data, whereas with the latter, random effects are ignored. The aim of this study was to develop LME, back propagation neural network (BPNN), and mixed-effects NN models that combine the 2 to predict FPG levels.

Monitoring data from 779 patients with T2DM from a multicentre, prospective study from the shared platform Figshare repository were divided 80/20 into training/test sets. The first 10 important features were modelled via random forest (RF) screening. First, an LME model was built to model interindividual differences, analyse the factors affecting FPG levels, compare the AIC and BIC values to screen the optimal model, and predict FPG levels. Second, multiple BPNN models were constructed via different variable sets to screen the optimal BPNN. Finally, an LME/BPNN combined model, named LMENN, was constructed via stacking integration. A 10-fold cross-validation cycle was performed using the training set to build the model and evaluate its performance, and then the final model was evaluated on the test set.

The top 10 variables screened by RF were HOMA-β, HbA1c, HOMA-IR, urinary sugar, insulin, BMI, waist circumference, weight, age, and group. The best-fitting random-intercept mixed-effects (lm22) model showed that each patient's baseline glucose levels influenced subsequent glucose measurements, but the trend over time was consistent. The LMENN model combines the strengths of LME and BPNN and accounts for random effects. The RMSE of the LMENN model ranges were 0.447-0.471 (training set), 0.525-0.552 (validation set), and 0.511-0.565 (test set). It improves the prediction performance of the single LME and BPNN models and shows some advantages in predicting FPG levels.

The LMENN model built by integrating LME and BPNN has several potential applications in analysing longitudinal FPG monitoring data. This study provides new ideas and methods for further research in the field of blood glucose prediction.