Abstract
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, 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 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 OrnsteinUhlenbeck (OU) and the square root models.
| Original language | English |
|---|---|
| Journal | Computational Statistics & Data Analysis |
| Volume | 55 |
| Issue number | 3 |
| Pages (from-to) | 1426-1444 |
| Number of pages | 19 |
| ISSN | 0167-9473 |
| Publication status | Published - 1 Mar 2011 |