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Using Hamiltonian Monte-Carlo to design longitudinal count studies accounting for parameter and model uncertainties Mentré, France


To design longitudinal studies with nonlinear mixed effect models (NLMEM), optimal design based on the expected Fisher information matrix (FIM) can be used. A new method evaluating the FIM based on Monte-Carlo Hamiltonian Monte-Carlo (MC/HMC) was developed and implemented in the R package MIXFIM using Stan for HMC sampling. This approach requires a priori knowledge on models and parameters, leading to locally optimal designs. The objective of this work was to extend this MC/HMC-based method to evaluate the FIM in NLMEM accounting for uncertainty in parameters and in models. We showed an illustration of this approach to optimize robust designs for repeated count data. When introducing uncertainty on the population parameters, we evaluated the robust FIM as the expectation of the FIM computed by MC/HMC on these parameters. Then, the compound D-optimality criterion was used to find a common CD-optimal design for several candidate models. A compound DE-criterion combining the determinants of the robust FIMs was also calculated to find the CDE-optimal design which was robust with respect to both model and parameters. These methods were applied in a longitudinal Poisson count model which event rate parameter (

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