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(10)

The PD model for drug effect is a simple Emax model with baseline, expressed as a function of the predicted concentrationsfPK, and given as follows for the sampling times tPD :

fPD(θPK,θPD,tPD)=E0+

where θPD=(E0,Emax,C50) is the vector of the PD parameters with E0, Emax andC50, the effect at baseline, the maximum effect and the concentration needed to observe half of the maximum effect, respectively.

We assumed an exponential model of the random effects for both the PK and the PD parameters. We associated a proportional error model with the PK model characterized by the parameter σslopePK and a homoscedastic error model with the PD model characterized by the parameter σinterPD. Thus, the vector of population parameters Ψ is described by the vector of the fixed effects βT=βCl,βV,βE,βE,βC and by λT the vector composed by the

C0max50variance of the random effects and by the parameters for the error models such that

22222

λT=(ωCl,ωV,ωE,ωE,ωC,σslopePK,σinterPD). The dose was fixed to 1 and the parameter

C

max

50

EmaxfPK(θPK,tPD)C50+fPK(θPK,tPD)

(13)

T

inserm-00371363, version 1 - 27 Mar 2009

()

values used in this paper are given in Table 1.

We determined a population design associated with this PKPD example. This determination was empirical, without any optimization. The population design was composed of one group of N=100 individuals. They all had 3 sampling times at 0.166, 6 and 12 for PK and 4 sampling times for PD at 0.166, 6, 12 and 20 hours. Therefore, we had one elementary design

(ξPK,ξPD) with ξPK=(0.166,6,12) and ξPD=(0.166,6,12,20). The population design was

thus defined byΞ= ξPK,ξPD,N . The curve profiles of the PK and the PD model for the

fixed effects are displayed in Figure 1; the sampling times for each response are overlaid.

2.4 Evaluation of MF for multiple responses

2.4.1 Comparison of MF with and without linearization

In this section, we propose to compare the predicted SE obtained from the approximate MF for multiple responses computed by PFIM 3.0 to the SE obtained from more “exact” approaches using the SAEM estimation algorithm. This latter algorithm was used by Retout et al. [20]

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