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- #Nonmem 3 compartment k too close to eigenvalue software#
- #Nonmem 3 compartment k too close to eigenvalue trial#
That the model parameter is estimable, as standard errors may beĬalculated using the R-matrix. In this case,Ĭomputational instability can lead to the misleading conclusion Matrix, this matrix can appear to be positive definite. However, due to the computational error in handling a singular if a model parameter is not estimable from the data),Ġ1/0 # 2016 American Association of Pharmaceutical Scientists Making the R-matrix of the reparameterised model as close to an
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Help reduce the misjudgement of the nature of the R-matrix by Will fail (when the model is, in fact, identifiable and the parametersĪre at the maximum likelihood). Model such as NONMEM, a user may encounter a message likeīR-matrix Algorithmically Singular and Non-Positive Semiĭefinite^ and the computation of the variance-covariance matrix
#Nonmem 3 compartment k too close to eigenvalue software#
Parameter estimation software for a non-linear mixed effects The positive definiteness of the R-matrix is a necessary conditionįor the estimated parameters to be at the maximum likelihood (cf.Īppendix A.3), if we are at the maximum likelihood, an R-matrix Influence pharmacometric analyses in two ways. InĪddition, an automated preconditioning routine is madeĪvailable as a part of the software package Perl-speaksNONMEM (PsN) version 4.4 and above (3).Ĭomputational instability related to the R-matrix can Of the existence of non-identifiable model parameters. When the R-matrix is fundamentally positive definite, andĬorrectly indicate a fundamentally singular R-matrix in case Reduce the failed variance-covariance matrix computations Our hypothesis is that preconditioning will Numerical experiments using published non-linear mixedĮ ff e c t s m o d e l s ( a nd d a t a ) f r o m a p p l i c a t i o n s i n To test this preconditioning method, we have conducted When the R-matrix is fundamentally singular. )īeing non-positive definite and also give an indication of To whom correspondence should be addressed. This approach should reduce the influence ofĬomputational issues and reduce the chance of the R-matrixĭepartment of Pharmaceutical Biosciences, Uppsala University,ĭepartment of Mathematics, Uppsala University, Uppsala, Sweden. (R-matrix) of the reparameterised model becomes close to an Model parameters so that the Hessian of the −2ln(likelihood) We reparameterise the model with a linear combination of the Preconditioning is a widely used technique to increase theĬomputational stability for numerically solving large sparse Non-linear mixed effects models to increase the computational stability of the variance-covariance matrix. In this paper, we propose a preconditioning method for The numerical method is based on finite precision The numerical stability of the computational algorithm when However, these estimates will unavoidably be influenced by That the parameter and uncertainty estimates of the nonlinear model are estimated correctly by a numerical method Pharmacometric analysis is usually based on the assumption Result, pharmacometric analysis based on non-linear mixedĮffects models, also known as the population approach, hasīecome an essential step in drug development.
#Nonmem 3 compartment k too close to eigenvalue trial#
Non-linear mixed effects models have been shown to beĪn effective tool for the analysis of clinical trial data. KEY WORDS: computational stability identifiability non-linear mixed effects model parameter Variance-covariance matrix computations, and reveal non-identifiability of the model parameters. We present numerical experimentsĭemonstrating that the stabilisation of the computation using the proposed method can recover failed This approach will reduce the influence of computational error, forĮxample rounding error, to the final computational result. Original model parameters so that the Hessian matrix of the likelihood of the reparameterised modelīecomes close to an identity matrix. Roughly speaking, the method reparameterises the model with a linear combination of the We propose a preconditioning method for non-linear mixedĮffects models used in pharmacometric analyses to stabilise the computation of the variance-covariance Starts to become a bottleneck in the analysis. Mathematical models are introduced and computational error resulting from computational instability As the importance of pharmacometric analysis increases, more and more complex Received 29 July 2015 accepted 4 January 2016Ībstract. Yasunori Aoki,1,2,3 Rikard Nordgren,1 and Andrew C. Of Variance-Covariance Matrix Computations Preconditioning of Nonlinear Mixed Effects Models for Stabilisation