Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics

Abstract

Stochastic differential equations (SDEs) are assuming an important role in the definition of dynamical models allowing for explanation of internal variability (stochastic noise).SDE models are well-established in many fields, such as investment finance, population dynamics, polymer dynamics, hydrology and neuronal models. The metabolism of glucose and insulin has not yet received much attention from SDE modellers, except from a few recent contributions, because of methodological and implementation difficulties in estimating SDE parameters. Objectives: here we propose a new SDE model for the dynamics of glycemia during a euglycemic hyperinsulinemic clamp experiment, introducing system noise in tissue glucose uptake, and apply for its estimation a closed-form Hermite expansion of the transition densities of the solution process. Results: the present work estimates the new model parameters using a computationally efficient approximate maximum likelihood approach. By comparison with other currently used methods, the estimation process is very fast, obviating the need to use clusters or expensive mainframes to obtain the quick answers needed for everyday iterative modeling. Furthermore, it can introduce the demonstrably essential concept of system noise in this branch of physiological modeling. Conclusions: SDE modeling for metabolic processes is physiologically pertinent and computationally feasible using commonly available resources.

Simulation and Parametric Inference of a Mixed Effects Model with Stochastic Differential Equations Using the Fokker-Planck Equation Solution

“…To apply the proposed methodology and evaluate its effectiveness, we consider the two-dimensional OU process that is very useful in pharmacokinetic/pharmacodynamic studies and in biology [43], physics, engineering, finance, and neuroscience applications [14,44]. Indeed, the choice of this process is due to the fact that it is one of the few known multivariate SDME models with known transition density.…”

Parametric inference for discrete observations of diffusion processes with mixed effects

“…Hence, SDEMEs provide a good framework to study population characteristics when longitudinal data are collected on multiple individuals ruled by the same intraindividual mechanisms (see e.g. Overgaard et al (2005), Ditlevsen and De Gaetano (2005b), Picchini et al (2008), Møller et al (2010), Donnet et al (2010), Berglund et al (2001), Leander et al (2015) for discussions and applications on real data sets).…”

Efficient estimation for diffusions sampled at high frequency over a fixed time interval

“…Diffusions given by stochastic differential equations find application in a number of fields where they are used to describe phenomena which evolve continuously in time. Some examples include agronomy (Pedersen, 2000), biology (Favetto and Samson, 2010), finance (Merton, 1971;Vasicek, 1977;Cox et al, 1985;Larsen and Sørensen, 2007) and neuroscience (Ditlevsen and Lansky, 2006;Picchini et al, 2008;Bibbona et al, 2010).…”