From: Nick Holford <*n.holford*>

Date: Mon, 17 Nov 2008 20:00:17 +1300

Xia,

I wrote:

*> 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?
*

*>
*

Leonid added:

*> CL = THETA(1) exp(THETA(2)*exp(ETA(1))) (2)
*

*>
*

*> But not every transformation is reasonable. I hardly can imagine the
*

*> case when you may want to use (2). Could you give some more realistic
*

*> examples, please, and situation when they were useful?
*

You replied but between

"Sorry, I did make myself clear."

and

"Sorry for any confusion!"

I only found unclear and confusing remarks (e.g. where is ETABAR actually used?)

Would you please focus more on answering our specific requests for an explicit NM-TRAN code fragment and justification for an apparently bizarre transformation and spend less time offering meaningless apologies?

Nick

XIA LI wrote:

*> Leonid,
*

*> Sorry, I did make myself clear.
*

*>
*

*> CL=THETA(1)*EXP(ETA(1)) (1)
*

*> where ETA(1) is Normal( 0, omega^2) or
*

*> log Normal(Eta_bar,omega^2)
*

*>
*

*> Adding one more stage means giving some functions for the MEAN and VARIANCE of ETA(1), say:
*

*>
*

*> Eta_bar=THETA(2)
*

*> omega^= THETA(3)*EXP(ETA(2)) (2)
*

*>
*

*> Sorry for any confusion!
*

*> Best,
*

*> Xia
*

*>
*

*>
*

*> ---- Original message ----
*

*>
*

*>> Date: Fri, 14 Nov 2008 18:37:22 -0500
*

*>> From: Leonid Gibiansky <LGibiansky *

*>> Subject: Re: [NMusers] Very small P-Value for ETABAR
*

*>> To: Xia Li <lix4 *

*>> Cc: "'Nick Holford'" <n.holford *

*>>
*

*>> Xia,
*

*>> I could be missing something but this
*

*>> ETA(1)= THETA(2)*exp(ETA(2)) (Eq. 1)
*

*>> does not make sense to me. In the original definition, ETA(1) is the
*

*>> random variable with normal distribution. Even if posthoc ETAs are not
*

*>> normal, they are still random. For example, it can be either positive or
*

*>> negative (unlike ETA1 given by (1)). If I the understood intentions
*

*>> correctly, this is an attempt to describe a transformation of the random
*

*>> effects to make it normal:
*

*>>
*

*>> CL = THETA(1) exp(ETA(1)) is replaced by
*

*>> CL = THETA(1) exp(THETA(2)*exp(ETA(1))) (2)
*

*>>
*

*>> But not every transformation is reasonable. I hardly can imagine the
*

*>> case when you may want to use (2). Could you give some more realistic
*

*>> examples, please, and situation when they were useful?
*

*>>
*

*>> On the separate note, mean of THETA(2)*exp(ETA(2)) is not equal to
*

*>> THETA(2): geometric mean of THETA(2)*exp(ETA(2)) is equal to THETA(2)
*

*>>
*

*>> Thanks
*

*>> Leonid
*

*>>
*

*>> --------------------------------------
*

*>> Leonid Gibiansky, Ph.D.
*

*>> President, QuantPharm LLC
*

*>> web: www.quantpharm.com
*

*>> e-mail: LGibiansky at quantpharm.com
*

*>> tel: (301) 767 5566
*

*>>
*

*>>
*

*>>
*

*>>
*

*>> Xia Li wrote:
*

*>>
*

*>>> Hi Nick,
*

*>>> My pleasure!
*

*>>>
*

*>>> This is a topic from Bayesian Hierarchical Model(BHM). If we look at the
*

*>>> simplest PK statement: CL=THETA(1)*EXP(ETA(1)), where ETA(1) is the between
*

*>>> subject random effect. We assume the "similarity" among the subjects may be
*

*>>> modeled by THETA(1) and ETA(1).
*

*>>>
*

*>>> Now here, if we observe that there is an underlying pattern between
*

*>>> ETA(1)'s, i.e. deviation from zero or no longer normal and we assume that
*

*>>> there is a similarity among those patterns.
*

*>>>
*

*>>> Since ETA(1)'s are assumed similar, it is reasonable to model the
*

*>>> "similarity" among the ETA(1)'s by THETA(2) and ETA(2): ETA(1)=
*

*>>> THETA(2)*exp(ETA(2)). Hence we have one more stage, ETA(1) now is
*

*>>> lognormal(nonsymmetrical) with mean THETA(2) (doesnt have to be zero).
*

*>>>
*

*>>> We will not say the variance of ETA(1) is confounded with the variance of
*

*>>> ETA(2), we say it is a function of variance of ETA(2).In statistics,
*

*>>> confounding means hard to distinguish from each other. Here, it is a direct
*

*>>> causation.
*

*>>>
*

*>>> Sorry I don't have a NM-TRAN code for this now. I usually use SAS and Win
*

*>>> bugs to do modeling and haven't tried this BHM in NONMEM. I will figure out
*

*>>> can I do it in NONMEM later.
*

*>>>
*

*>>> Best,
*

*>>> Xia
*

*>>>
*

*>>> -----Original Message-----
*

*>>> From: owner-nmusers *

*>>> Behalf Of Nick Holford
*

*>>> Sent: Friday, November 14, 2008 3:34 PM
*

*>>> To: nmusers
*

*>>> Subject: Re: [NMusers] Very small P-Value for ETABAR
*

*>>>
*

*>>> 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
*

*>>>>
*

*>>>>
*

*> ======================================
*

*> 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 Mon Nov 17 2008 - 02:00:17 EST

Date: Mon, 17 Nov 2008 20:00:17 +1300

Xia,

I wrote:

Leonid added:

You replied but between

"Sorry, I did make myself clear."

and

"Sorry for any confusion!"

I only found unclear and confusing remarks (e.g. where is ETABAR actually used?)

Would you please focus more on answering our specific requests for an explicit NM-TRAN code fragment and justification for an apparently bizarre transformation and spend less time offering meaningless apologies?

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 Mon Nov 17 2008 - 02:00:17 EST