CORR MATRIX NONMEM SOFTWARE
For example when using a parameter estimation software for a non-linear mixed effects model such as NONMEM, a user may encounter a message like “R-matrix Algorithmically Singular and Non-Positive Semi Definite” and the computation of the variance-covariance matrix will fail (when the model is, in fact, identifiable and the parameters are at the maximum likelihood). Appendix A.3), if we are at the maximum likelihood, an R-matrix may appear to be non-positive definite. First, given that the positive definiteness of the R-matrix is a necessary condition for the estimated parameters to be at the maximum likelihood ( cf. In addition, an automated preconditioning routine is made available as a part of the software package Perl-speaks-NONMEM (PsN) version 4.4 and above ( 3).Ĭomputational instability related to the R-matrix can influence pharmacometric analyses in two ways. Our hypothesis is that preconditioning will reduce the failed variance-covariance matrix computations when the R-matrix is fundamentally positive definite, and correctly indicate a fundamentally singular R-matrix in case of the existence of non-identifiable model parameters. To test this preconditioning method, we have conducted numerical experiments using published non-linear mixed effects models (and data) from applications in pharmacometrics. This approach should reduce the influence of computational issues and reduce the chance of the R-matrix being non-positive definite and also give an indication of when the R-matrix is fundamentally singular. Inspired by this technique, we reparameterise the model with a linear combination of the model parameters so that the Hessian of the −2ln(likelihood) (R-matrix) of the reparameterised model becomes close to an identity matrix. Preconditioning is a widely used technique to increase the computational stability for numerically solving large sparse systems of linear equations ( 1, 2). In this paper, we propose a preconditioning method for non-linear mixed effects models to increase the computational stability of the variance-covariance matrix. The pharmacometric analysis is usually based on the assumption that the parameter and uncertainty estimates of the non-linear model are estimated correctly by a numerical method however, these estimates will unavoidably be influenced by the numerical stability of the computational algorithm when the numerical method is based on finite precision computations. As a result, pharmacometric analysis based on non-linear mixed effects models, also known as the population approach, has become an essential step in drug development.
CORR MATRIX NONMEM TRIAL
Non-linear mixed effects models have been shown to be an effective tool for the analysis of clinical trial data.
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