Stochastic differential mixed-effects models
U. Picchini, A. De Gaetano and S. Ditlevsen
Published on Scandinavian Journal of Statistics (2010), 37(1), 67-90.
See also the corresponding Corrigendum.
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Stochastic differential equations have shown useful to describe random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered
and variability between experimental units, thus providing a powerful modeling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies.
In most cases the likelihood function is not available, and thus maximum likelihood estimation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real datasets.
Keywords: biomedical applications; Brownian motion with drift; CIR process; closed-form transition density expansion; Gaussian quadrature; geometric Brownian motion; maximum likelihood estimation; Ornstein-Uhlenbeck process; random parameters; stochastic differential equations.
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