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- Aoki, Yasunori, 1982-, et al.
(författare)
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Cluster Gauss-Newton method : An algorithm for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models
- 2022
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Ingår i: Optimization and Engineering. - : Springer. - 1389-4420 .- 1573-2924. ; 23:1, s. 169-199
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Tidskriftsartikel (refereegranskat)abstract
- Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiser obtained using these iterative methods usually depends on the choice of the initial iterate. Thus, the estimated parameter and subsequent analyses using it depend on the choice of the initial iterate. One way to reduce the analysis bias due to the choice of the initial iterate is to repeat the algorithm from multiple initial iterates (i.e. use a multi-start method). However, the procedure can be computationally intensive and is not always used in practice. To overcome this problem, we propose the Cluster Gauss-Newton (CGN) method, an efficient algorithm for finding multiple approximate minimisers of nonlinear-least squares problems. CGN simultaneously solves the nonlinear least squares problem from multiple initial iterates. Then, CGN iteratively improves the approximations from these initial iterates similarly to the Gauss-Newton method. However, it uses a global linear approximation instead of the Jacobian. The global linear approximations are computed collectively among all the iterates to minimise the computational cost associated with the evaluation of the mathematical model. We use physiologically based pharmacokinetic (PBPK) models used in pharmaceutical drug development to demonstrate its use and show that CGN is computationally more efficient and more robust against local minima compared to the standard Levenberg-Marquardt method, as well as state-of-the art multi-start and derivative-free methods.
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- Aoki, Yasunori, 1982-, et al.
(författare)
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Cluster Newton Method for Sampling Multiple Solutions of Underdetermined Inverse Problems : Application to a Parameter Identification Problem in Pharmacokinetics
- 2014
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Ingår i: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 36:1, s. B14-B44
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Tidskriftsartikel (refereegranskat)abstract
- A new algorithm is proposed for simultaneously finding multiple solutions of an underdetermined inverse problem. The algorithm was developed for an ODE parameter identification problem in pharmacokinetics for which multiple solutions are of interest. The algorithm proceeds by computing a cluster of solutions simultaneously, and is more efficient than algorithms that compute multiple solutions one-by-one because it fits the Jacobian in a collective way using a least squares approach. It is demonstrated numerically that the algorithm finds accurate solutions that are suitably distributed, guided by a priori information on which part of the solution set is of interest, and that it does so much more efficiently than a baseline Levenberg-Marquardt method that computes solutions one-by-one. It is also demonstrated that the algorithm benefits from improved robustness due to an inherent smoothing provided by the least-squares fitting.
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- Aoki, Yasunori, 1982-, et al.
(författare)
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Model selection and averaging of nonlinear mixed-effect models for robust phase III dose selection
- 2017
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Ingår i: Journal of Pharmacokinetics and Pharmacodynamics. - : Springer Science and Business Media LLC. - 1567-567X .- 1573-8744. ; 44:6, s. 581-597
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Tidskriftsartikel (refereegranskat)abstract
- Population model-based (pharmacometric) approaches are widely used for the analyses of phase IIb clinical trial data to increase the accuracy of the dose selection for phase III clinical trials. On the other hand, if the analysis is based on one selected model, model selection bias can potentially spoil the accuracy of the dose selection process. In this paper, four methods that assume a number of pre-defined model structure candidates, for example a set of dose-response shape functions, and then combine or select those candidate models are introduced. The key hypothesis is that by combining both model structure uncertainty and model parameter uncertainty using these methodologies, we can make a more robust model based dose selection decision at the end of a phase IIb clinical trial. These methods are investigated using realistic simulation studies based on the study protocol of an actual phase IIb trial for an oral asthma drug candidate (AZD1981). Based on the simulation study, it is demonstrated that a bootstrap model selection method properly avoids model selection bias and in most cases increases the accuracy of the end of phase IIb decision. Thus, we recommend using this bootstrap model selection method when conducting population model-based decision-making at the end of phase IIb clinical trials.
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- Aoki, Yasunori, 1982-, et al.
(författare)
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Numerical study of unbounded capillary surfaces
- 2014
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Ingår i: Pacific Journal of Mathematics. - : Mathematical Sciences Publishers. - 0030-8730 .- 1945-5844. ; 267:1, s. 1-34
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Tidskriftsartikel (refereegranskat)abstract
- Unbounded capillary surfaces in domains with a sharp corner or a cusp are studied. It is shown how numerical study using a proposed computational methodology leads to two new conjectures for open problems on the asymptotic behavior of capillary surfaces in domains with a cusp. The numerical methodology contains two simple but important ingredients, a change of variable and a change of coordinates, which are inspired by known asymptotic approximations for unbounded capillary surfaces. These ingredients are combined with the finite volume element or Galerkin finite element methods. Extensive numerical tests show that the proposed computational methodology leads to a global approximation method for singular solutions of the Laplace–Young equation that recovers the proper asymptotic behavior at the singular point, is more accurate and has better convergence properties than numerical methods considered for singular capillary surfaces before. Using this computational methodology, two open problems on the asymptotic behavior of capillary surfaces in domains with a cusp are studied numerically, leading to two conjectures that may guide future analytical work on these open problems.
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- Aoki, Yasunori, 1982-, et al.
(författare)
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PopED lite : an optimal design software for preclinical pharmacokinetic and pharmacodynamic studies
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Optimal experimental design approaches are seldom used in pre-clinical drug discovery. Main reasons for this lack of use are that available software tools require relatively high insight in optimal design theory, and that the design-execution cycle of in vivo experiments is short, making time-consuming optimizations infeasible. We present the publicly available software PopED lite in order to increase the use of optimal design in pre-clinical drug discovery. PopED lite is designed to be simple, fast and intuitive. Simple, to give many users access to basic optimal design calculations. Fast, to fit the short design-execution cycle and allow interactive experimental design (test one design, discuss proposed design, test another design, etc). Intuitive, so that the input to and output from the software can easily be understood by users without knowledge of the theory of optimal design. In this way, PopED lite is highly useful in practice and complements existing tools. Key functionality of PopED lite is demonstrated by three case studies from real drug discovery projects.
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- Aoki, Yasunori, et al.
(författare)
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PopED lite: an optimal design software for preclinical pharmacokinetic and pharmacodynamic studies
- 2016
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Ingår i: Computer Methods and Programs in Biomedicine. - : Elsevier BV. - 0169-2607 .- 1872-7565. ; 127, s. 126-143
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Tidskriftsartikel (refereegranskat)abstract
- Background and ObjectiveOptimal experimental design approaches are seldom used in preclinical drug discovery. The objective is to develop an optimal design software tool specifically designed for preclinical applications in order to increase the efficiency of drug discovery in vivo studies.MethodsSeveral realistic experimental design case studies were collected and many preclinical experimental teams were consulted to determine the design goal of the software tool. The tool obtains an optimized experimental design by solving a constrained optimization problem, where each experimental design is evaluated using some function of the Fisher Information Matrix. The software was implemented in C++ using the Qt framework to assure a responsive user-software interaction through a rich graphical user interface, and at the same time, achieving the desired computational speed. In addition, a discrete global optimization algorithm was developed and implemented.ResultsThe software design goals were simplicity, speed and intuition. Based on these design goals, we have developed the publicly available software PopED lite (http://www.bluetree.me/PopED_lite). Optimization computation was on average, over 14 test problems, 30 times faster in PopED lite compared to an already existing optimal design software tool. PopED lite is now used in real drug discovery projects and a few of these case studies are presented in this paper.ConclusionsPopED lite is designed to be simple, fast and intuitive. Simple, to give many users access to basic optimal design calculations. Fast, to fit a short design-execution cycle and allow interactive experimental design (test one design, discuss proposed design, test another design, etc). Intuitive, so that the input to and output from the software tool can easily be understood by users without knowledge of the theory of optimal design. In this way, PopED lite is highly useful in practice and complements existing tools.
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- Aoki, Yasunori, et al.
(författare)
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Preconditioning of Nonlinear Mixed Effects Models for Stabilisation of Variance-Covariance Matrix Computations
- 2016
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Ingår i: AAPS Journal. - : Springer Science and Business Media LLC. - 1550-7416. ; 18:2, s. 505-518
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Tidskriftsartikel (refereegranskat)abstract
- As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and computational error resulting from computational instability starts to become a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix. Roughly speaking, the method reparameterises the model with a linear combination of the original model parameters so that the Hessian matrix of the likelihood of the reparameterised model becomes close to an identity matrix. This approach will reduce the influence of computational error, for example rounding error, to the final computational result. We present numerical experiments demonstrating that the stabilisation of the computation using the proposed method can recover failed variance-covariance matrix computations, and reveal non-identifiability of the model parameters.
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