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(6)

2 Methods

2.1 Notation

In the nonlinear mixed effect multiple response model, an “elementary” design ξi for one individual i is defined by nisampling times. It is composed of several sub-designs such that

ξi=(ξi1,ξi2,K,ξiK), with ξik being the sub-design associated with the kth response,

k=1,K,K. ξik is defined by tik1,tik2,K,tiknik, the vector of the nik sampling times for the

()

observations of the k response, so that ni=∑nik.

th

K

k=1

For N individuals, we define a “population design” composed of the N allocated elementary

inserm-00371363, version 1 - 27 Mar 2009

designs ξi, i=1,K,N. A population design is therefore described by the N elementary designs for a total number n of observations such that n=∑ni:

i=1N

Ξ={ξ1,K,ξN}

(1)

Usually population designs are composed of a limited number Q of groups of individuals with identical design within each group. Each of these groups is defined by an elementary designξq,q=1,K,Q, which is composed, for the kthresponse, of nqk sampling times

(t

qk1

,tqk2,K,tqknqk to be performed in a number Nq of individuals. The population design can

)

then be written as follows:

Ξ=[ξ1,N1];[ξ2,N2];K; ξQ,NQ

{}

(2)

A nonlinear mixed effects multiple response model or a multiple response population model is defined as follows. The vector of observations Yi for the ith individual is defined as the vector of the K different responses:

TTT

Yi= y,y,K,yi1i1iK

T

(3)

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