المؤلفون: Ueckert, Sebastian, Mentré, France

المصدر: Elsevier, Computational Statistics & Data Analysis. 111(C):203-219

الوصف: The design of experiments for discrete mixed effect models is challenging due to the unavailability of a closed-form expression for the Fisher information matrix (FIM), on which most optimality criteria depend. Existing approaches for the computation of the FIM for those models are all based on approximations of the likelihood. A new method is presented which is based on derivatives of the exact conditional likelihood and which uses Monte Carlo (MC) simulations as well as adaptive Gaussian quadrature (AGQ) to integrate those derivatives over the data and random effects. The method is implemented in R and evaluated with respect to the influence of the tuning parameter, the accuracy of the FIM approximation, and computational complexity. The accuracy evaluation is performed by comparing the expected relative standard errors (RSE) from the MC/AGQ FIM with RSE obtained in a simulation study with four different discrete data models (two binary, one count and one repeated time-to-event model) and three different estimation algorithms. Additionally, the results from the MC/AGQ FIM are compared with expected RSE from a marginal quasi-likelihood (MQL) approximated FIM. The comparison resulted in close agreement between the MC/AGQ-based RSE and empirical RSE for all models investigated, and better performance of MC/AGQ than the MQL approximated FIM for variance parameters. The MC/AGQ method also proved to be well suited to calculate the expected power to detect a group effect for a model with binary outcomes.

الإتاحة: https://ideas.repec.org/a/eee/csdana/v111y2017icp203-219.html

المؤلفون: Nguyen, Thu Thuy, Mentré, France

المصدر: Elsevier, Computational Statistics & Data Analysis. 80(C):57-69

الوصف: Nonlinear mixed effect models (NLMEM) are used in model-based drug development to analyse longitudinal data. To design these studies, the use of the expected Fisher information matrix (MF) is a good alternative to clinical trial simulation. Presently, MF in NLMEM is mostly evaluated with first-order linearisation. The adequacy of this approximation is, however, influenced by model nonlinearity. Alternatives for the evaluation of MF without linearisation are proposed, based on Gaussian quadratures. The MF, expressed as the expectation of the derivatives of the log-likelihood, can be obtained by stochastic integration. The likelihood for each simulated vector of observations is approximated by Gaussian quadrature centred at 0 (standard quadrature) or at the simulated random effects (adaptive quadrature). These approaches have been implemented in R. Their relevance was compared with clinical trial simulation and linearisation, using dose–response models, with various nonlinearity levels and different number of doses per patient. When the nonlinearity was mild, three approaches based on MF gave correct predictions of standard errors, when compared with the simulation. When the nonlinearity increased, linearisation correctly predicted standard errors of fixed effects, but over-predicted, with sparse designs, standard errors of some variability terms. Meanwhile, quadrature approaches gave correct predictions of standard errors overall, but standard Gaussian quadrature was very time-consuming when there were more than two random effects. To conclude, adaptive Gaussian quadrature is a relevant alternative for the evaluation of MF for models with stronger nonlinearity, while being more computationally efficient than standard quadrature.

الإتاحة: https://ideas.repec.org/a/eee/csdana/v80y2014icp57-69.html