Stochastic Differential Mixed-Effects Models |
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Authors: | UMBERTO PICCHINI REA DE GAETANO SUSANNE DITLEVSEN |
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Institution: | Department of Mathematical Sciences, University of Copenhagen;Biomathematics Laboratory, IASI–CNR; Biomathematics Laboratory (BioMatLab) IASI–CNR; Department of Mathematical Sciences, University of Copenhagen |
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Abstract: | Abstract. Stochastic differential equations have been shown useful in describing 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 modelling 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 data sets. |
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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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