Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model considers measurement error not only in treatment covariates, but also in treatment times, a problem which arises in practice for example when treatment information is based on self-reporting. In a challenging and timely problem of estimating the impact of diet on continuous blood glucose measurements, our model leads to significant improvements in estimation accuracy and prediction.
: In contrast to the data-driven approaches used in machine learning, mechanistic models use substantial knowledge of a specific problem to characterize the system with differential equations, and inference is done for example using filtering algorithms. Similar to our application, @cite_4 and @cite_41 study blood glucose dynamics, affected by nutrition and other factors. Another example is a computational model of the physiological mechanisms for type-2 diabetes, aiming to quantify factors useful for prevention of the disease @cite_39 .
@cite_41 @cite_4 @cite_39
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Type 2 diabetes leads to premature death and reduced quality of life for 8 of Americans. Nutrition management is critical to maintaining glycemic control, yet it is difficult to achieve due to the high individual differences in glycemic response to nutrition. Anticipating glycemic impact of different meals can be challenging not only for individuals with diabetes, but also for expert diabetes educators. Personalized computational models that can accurately forecast an impact of a given meal on an individual’s blood glucose levels can serve as the engine for a new generation of decision support tools for individuals with diabetes. However, to be useful in practice, these computational engines need to generate accurate forecasts based on limited datasets consistent with typical self-monitoring practices of individuals with type 2 diabetes. This paper uses three forecasting machines: (i) data assimilation, a technique borrowed from atmospheric physics and engineering that uses Bayesian modeling to infuse data with human knowledge represented in a mechanistic model, to generate real-time, personalized, adaptable glucose forecasts; (ii) model averaging of data assimilation output; and (iii) dynamical Gaussian process model regression. The proposed data assimilation machine, the primary focus of the paper, uses a modified dual unscented Kalman filter to estimate states and parameters, personalizing the mechanistic models. Model selection is used to make a personalized model selection for the individual and their measurement characteristics. The data assimilation forecasts are empirically evaluated against actual postprandial glucose measurements captured by individuals with type 2 diabetes, and against predictions generated by experienced diabetes educators after reviewing a set of historical nutritional records and glucose measurements for the same individual. The evaluation suggests that the data assimilation forecasts compare well with specific glucose measurements and match or exceed in accuracy expert forecasts. We conclude by examining ways to present predictions as forecast-derived range quantities and evaluate the comparative advantages of these ranges. Abstract Personalized mechanistic models involving exercise, meal and insulin interventions for type 1 diabetic children and adolescents are not commonly seen in the literature. Patient specific variations in blood glucose homeostasis and adverse effects of exercise-induced hypoglycemia emphasize the need for personalized models. Hence, a modified mechanistic model for exercise, meal and insulin interventions is proposed and tailored as personalized models for 34 type 1 diabetic children and adolescents. This is achieved via a 3-stage methodology comprising of modification, a priori identifiability analysis, and personalized parameter estimation and validation using the clinical data. Rate of perceived exertion is introduced as a marker quantifying exercise intensity. Six out of 16 parameters in the modified model are identified to be estimable and are estimated for each subject as personalized parameters. The R 2 values for both fitness and validation vary between 0.7 and 0.96 in 97 of the patients, indicating the goodness of the proposed model in explaining the glucose dynamics. For most of the estimated parameters, values of personalized point estimates and their confidence intervals are found to be within physiological ranges reported in the modeling literature. Personalized values of appearance rate of exercise effect on glucose uptake in 34 subjects are 54–250 higher than the nominal values of adults. This is expected for children and adolescents as the literature shows that they exhibit higher fat and exogenous carbohydrate oxidation rates during exercise when compared to adults. A computational model of the physiological mechanisms driving an individual's health towards onset of type 2 diabetes (T2D) is described, calibrated and validated using data from the Diabetes Prevention Program (DPP). The objective of this model is to quantify the factors that can be used for prevention of T2D. The model is energy and mass balanced and continuously simulates trajectories of variables including body weight components, fasting plasma glucose, insulin, and glycosylated hemoglobin among others on the time-scale of years. Modeled mechanisms include dynamic representations of intracellular insulin resistance, pancreatic beta-cell insulin production, oxidation of macronutrients, ketogenesis, effects of inflammation and reactive oxygen species, and conversion between stored and activated metabolic species, with body-weight connected to mass and energy balance. The model was calibrated to 331 placebo and 315 lifestyle-intervention DPP subjects, and one year forecasts of all individuals were generated. Predicted population mean errors were less than or of the same magnitude as clinical measurement error; mean forecast errors for weight and HbA1c were 5 , supporting predictive capabilities of the model. Validation of lifestyle-intervention prediction is demonstrated by synthetically imposing diet and physical activity changes on DPP placebo subjects. Using subject level parameters, comparisons were made between exogenous and endogenous characteristics of subjects who progressed toward T2D (HbA1c > 6.5) over the course of the DPP study to those who did not. The comparison revealed significant differences in diets and pancreatic sensitivity to hyperglycemia but not in propensity to develop insulin resistance. A computational experiment was performed to explore relative contributions of exogenous versus endogenous factors between these groups. Translational uses to applications in public health and personalized healthcare are discussed.