with,
E(Yi) Ei=F(g(β,0),ξi) (10)
FT(g(β,0),ξi) F(g(β,0),ξi)
Var(Yi) Vi= +Σ(β,0,σinter,σslope,ξi) T b b
This expression has been implemented in an extension of the R function PFIM, PFIM 3.0. This function has been developed for R 2.4.1 and higher versions. The implementation of the population Fisher information matrix assumes that the variance of the observations with
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inserm-00371363, version 1 - 27 Mar 2009
respect to the mean parameters is constant (see Appendix). PFIM 3.0 evaluates population designs in NLMEM with multiple responses and thus returns the expected standard errors, defined as the square roots of the diagonal elements of the inverse of MF, on the population parameters with the design evaluated. To use PFIM 3.0, some prior information has to be supplied by the user such as the structural model, its parameterization and a priori values of the parameters. PFIM 3.0 can also optimize population designs with different optimization options. More details are available in an extensive document that can be freely downloaded with the function PFIM 3.0 on the PFIM website [21].
2.3 PKPD simulation example
In this paper, we use a simple and typical PKPD model as an example to evaluate MF by simulation. It is derived from the one used by Hooker et al. [25] to illustrate the development of the Fisher information matrix for a multiple response model. The PK model for drug concentration is a one compartment with bolus input and first order elimination given as follows for the sampling time tPK:
fPK(θPK,tPK)=
where θPK=(Cl,VC)is the vector of the PK parameters with Cl and VC, the clearance and the volume in the central compartment, respectively.
T
doseCl
exp( tPK) VCVC
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