Practical estimation of high dimensional stochastic differential mixed-effects models

Stochastic differential equations (SDEs) are established tools for modeling 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 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 for modeling 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 (C) 2010 Elsevier B V All rights reserved