Fisher信息矩阵用于非线性混合效应的多重效应模型：用于的药代动(8)

diagonal matrix composed of each diagonal element of Σik with k=1,K,K. σslope and σinter are two vectors of the K components σinterk and σslopek, k=1,K,K, respectively. Finally, conditionally on the value of bi, we assume that the errors εi are independently distributed. Let Ψ be the vector of population parameters to be estimated such as

2

ΨT=(βT,ω12,K,ωp,σinterT,σslopeT) and let λ be the vector of variance 2

,σinterT,σslopeT), so that ΨT=(βT,λT). termsλT=(ω12,K,ωp

2.2 Population Fisher information matrix for multiple response models

The population Fisher information matrix for a population design Ξ (see Equation (1)), is

inserm-00371363, version 1 - 27 Mar 2009

defined as the sum of the N elementary Fisher information matrices MF(Ψ,ξi) for each individual i:

N

MF(Ψ,Ξ)=∑MF(Ψ,ξi)

i=1

(7)

In the case of a limited number Q of groups, as in Equation (2), it is expressed by:

Q

MF(Ψ,Ξ)=∑NqMF(Ψ,ξq)

q=1

(8)

The expression of an elementary Fisher information matrix for multiple responses has been extended by Hooker et al. [25] using the same development as for single response models with a first Taylor expansion of the model as in Mentré et al. [17] and Retout et al. [22]. Its expression is given below for one individual iand depends on the approximated marginal expectation Ei and variance Viof the observationsYi [28]. Details of this development are given in the Appendix.

EiT 1 Ei1 1 Vi 1 Vi

MF(Ψ,ξi)=V+tr ViV

Ψm Ψl2 Ψm Ψl

with m and l=1,K,dim(Ψ). (9)

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