From: Nick Holford <*n.holford*>

Date: Sat, 15 Nov 2008 09:33:40 +1300

Jakob, Mats,

Thanks very much for your careful explanations of how asymmetric EBE

distributions can arise. That is very helpful for my understanding.

Xia,

I am intrigued by your suggestion for how to estimate and account for

the bias in the mean of the EBE distribution.

In the usual ETA on EPS model I might write:

; SD of residual error for mixed proportional and additive random effects

PROP=THETA(1)*F

ADD=THETA(2)

SD=SQRT(PROP*PROP + ADD*ADD)

Y=F + EPS(1)*SD*EXP(ETA(1))

where EPS(1) is distributed mean zero, variance 1 FIXED

and ETA(1) is the between subject random effect for residual error

You seem to be suggesting:

ETABAR=THETA(3)

Y=F + EPS(1)*SD*EXP(ETA(1)) * ETABAR*EXP(ETA(2))

It seems to me that the variance of ETA(1) will be confounded with the

variance of ETA(2). Would you please explain more clearly (with an

explicit NM-TRAN code fragment if possible) what you are suggesting?

Best wishes,

Nick

Xia Li wrote:

*> Hi Jakob,
*

*> Thank you very much for the information adding an "eta on epsilon". This is
*

*> what I did in my research and I am glad to see people in Pharmacometrics is
*

*> using it.
*

*>
*

*> And in Bayesian analysis, adding one more stage for ETA, i.e
*

*> ETA=ETABAR*exp(eta2), eta2~N(0,omega2) will allow the deviation from zero
*

*> and shrinkage of ETA.
*

*>
*

*> Again, thanks all for your input.:)
*

*>
*

*> Best Regards,
*

*> Xia
*

*>
*

*> Xia Li
*

*> Mathematical Science Department
*

*> University of Cincinnati
*

*>
*

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Fri Nov 14 2008 - 15:33:40 EST

Date: Sat, 15 Nov 2008 09:33:40 +1300

Jakob, Mats,

Thanks very much for your careful explanations of how asymmetric EBE

distributions can arise. That is very helpful for my understanding.

Xia,

I am intrigued by your suggestion for how to estimate and account for

the bias in the mean of the EBE distribution.

In the usual ETA on EPS model I might write:

; SD of residual error for mixed proportional and additive random effects

PROP=THETA(1)*F

ADD=THETA(2)

SD=SQRT(PROP*PROP + ADD*ADD)

Y=F + EPS(1)*SD*EXP(ETA(1))

where EPS(1) is distributed mean zero, variance 1 FIXED

and ETA(1) is the between subject random effect for residual error

You seem to be suggesting:

ETABAR=THETA(3)

Y=F + EPS(1)*SD*EXP(ETA(1)) * ETABAR*EXP(ETA(2))

It seems to me that the variance of ETA(1) will be confounded with the

variance of ETA(2). Would you please explain more clearly (with an

explicit NM-TRAN code fragment if possible) what you are suggesting?

Best wishes,

Nick

Xia Li wrote:

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Fri Nov 14 2008 - 15:33:40 EST