Table 1.
Summary of the diabetes dataset.
Fig 1.
Graphical model of the probabilistic model.
Observed variables are the i insulin injections, pa physical activity events, m meal intakes, t time, glucose measurements,
subcutaneous glucose concentration, and
heart rate measurements.
is the effect of the insulin, RA is the rate of glucose absorption from the carbohydrate intake, PA is the effect of physical activity on the insulin sensitivity,
is the glucose distribution volume. Parameters vary in terms of number of levels of estimation, but there are four distinct levels: cohort, patient, sample (corresponding to a 24h-long window), and event (such as physical activity, meal intake, or insulin injection). Table 2 details the latent variables and their estimation method. The deterministic submodels (in diamonds) are differential equations solved by numerical integration or through their analytical impulse response.
Table 2.
Summary for the latent and observed variables of the model.
Table 3.
Prior distributions.
Fig 2.
24h-long sample from the dataset (CGM, meal intake, insulin, physical activity) for prior predictive checks.
Colored lines are random samples from the prior predictive distribution. a) The prior predictive distribution spans the 0-400 mg/dL physiologically relevant space. b) Prior predictive distribution when conditioning on zero insulin and meal intake. Glucose in such scenarios is expected to rise to approximately 400 mg/dL where ketones are dominantly produced, and renal excretion is also active.
Fig 3.
Exemplary fitted posterior predictive glucose trajectories for all the patients.
Solid blue line shows the CGM measurements, black dashed line the posterior mean of the subcutaneous glucose, blue dashed line the coefficient of insulin sensitivity driven by physical activity, red line shows the rate of glucose appearance, green line shows the total effect of insulin.
Table 4.
Root-mean-square error (mg/dL) between the CGM measurements and the mean of the posterior predictive distribution.
Fig 4.
Samples from the posterior distributions of EGP and SI.
One concentrated region belongs to a 24h-long patient sample.
Table 5.
Posterior means and 95% credible intervals for the parameters which affect interday variability.
Fig 5.
Histograms of the aggregated posterior samples of the variables related to the self-reported meals.
The meal coefficients here are represented according to the 0.8-1.0 range of glucose bioavailability; the model was fitted assuming a bioavailability of 0.8.
Table 6.
Post-hoc analysis of the meal-related parameters with respect to macronutritional composition and glucose level at the self-reported time.
Fig 6.
Histograms of the aggregated posterior samples of the variables related to the self-reported physical activities.
The gain and the time constant differ between short and long effect, while the start offset was assumed to be the same. The lower subplot depicts aggregate effect of the posteriors.
Fig 7.
Posterior predictive checks with generating new EGP, SI, and intraday variability.
The shaded area represent the 10-90 percentile of the resulting distribution. The black dashed line is the mean of the fitted posterior predictive distribution. The histogram compares the predictive distribution with different levels of uncertainty to the real-world CGM distribution. Yellow predictive intervals represent the uncertainty band caused by variability in the posterior parameters and intraday variation. The blue uncertainty band, in addition to intraday variability, also captures interday variability, which further inflates the bands.
Table 7.
Posterior predictive checks for all the participants based on glucose levels.