Practical Estimation of High Dimensional Stochastic Differential Mixed-Effects Models

TL;DR

This paper introduces a new framework combining stochastic differential equations with mixed-effects models to analyze population dynamics affected by randomness, with applications in biomedical fields.

Contribution

It proposes a novel stochastic differential mixed-effects modeling framework and an estimation method, along with computational guidelines for efficient implementation.

Findings

Method successfully estimates parameters in simulated models.

Framework distinguishes between population variability and individual stochasticity.

Applicable to pharmacokinetics and biomedical modeling.

Abstract

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified and separated from the drift itself. When it is of interest to model dynamics within a given population, i.e. to model simultaneously the performance of several experiments or subjects, mixed-effects modelling allows for the distinction of between and within experiment variability. A framework to model dynamics within a population using SDEs is proposed, representing simultaneously several sources of variation: variability between experiments using a mixed-effects approach and stochasticity in the individual dynamics using SDEs. These "stochastic differential mixed-effects models" have applications in e.g. pharmacokinetics/pharmacodynamics and biomedical modelling. A parameter estimation method is proposed and computational guidelines for an efficient implementation are given. Finally the method is evaluated using simulations from standard models like the two-dimensional Ornstein-Uhlenbeck (OU) and the square root models.