Abstract
Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is challenging. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference (up to the discretisation of the stochastic differential equation) is possible using particle MCMC methods. Although the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. Our article develops three extensions to the naive approach which exploit specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on simulated data and data from a tumour xenography study on mice.
Highlights
Stochastic differential equations (SDEs) are defined as ordinary differential equations (ODEs) with one or more stochastic components
Parallelisation is only applied if the average number of observations per subject is greater than 10, and it is not used for component-wise pseudo-marginal (CWPM) and Mixed particle method (MPM) on the Particle Methods for stochastic differential equation (SDE) mixed effects model (SDEMEM) sim(10, 24) dataset as it increased the computation time
Once we started testing combinations, we found that the variance of the LaplaceODE importance density approaches 0 for at least one of the random effects, such that the draws for that random effect are approximately equal
Summary
Stochastic differential equations (SDEs) are defined as ordinary differential equations (ODEs) with one or more stochastic components. SDEs allow for random variations around the mean dynamics specified by the ODE. These models can be used to capture inherent randomness in the system of interest. SDEMEMs are emerging as a useful class of models for biomedical and pharmacokinetic/pharmacodynamic data (Donnet et al, 2010; Donnet and Samson, 2013a; Leander et al, 2015). They have been applied in psychology (Oravecz et al, 2011) and spatio-temporal modelling (Duan et al, 2009).
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