Continuation of discussion from thread 99aug052003.html

From: Yaning Wang <yaning@ufl.edu>
Subject: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/7/2003 11:37 AM

Dear Rick:

Based on the code provided about flip-flop, the constrain is to make sure
every individual's Ka>Ke.
Can we use the following code to "estimate" TVKA and its between-subject
variability? The only problem will be the SE of TVKA, which can be
approximated by delta method based on the SEs of theta1, theta2 and theta3.
I know that this code cannot guarantee every subject's Ka>Ke. But with
TVKa>TVKe, what is the chance of some individuals' Ka<Ke?

CL=THETA(1)*EXP(ETA(1))
V=THETA(2)*EXP(ETA(2))
TVKE=THETA(1)/THETA(2)
TVKA=TVKE+THETA(3)
KA=TVKA*EXP(ETA(3))

Yaning Wang
Department of Pharmaceutics
College of Pharmacy
University of Florida

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From:  Ken Kowalski <Ken.Kowalski@pfizer.com>
Subject: RE: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/7/2003 1:32 PM

All,

This parameterization (TVKA>TVKE) will ensure that the population estimates
don't flip-flop.  At the individual level flip-flop might still occur.
Flip-flop at the individual level is more likely to occur when the
population estimates for ka and ke are fairly close relative to the IIV.  If
we have about an order of magnitude difference between ka and ke and the IIV
for ka, CL, and V are not too large we are less likely to have flip-flop.
Still, it is probably good practice to routinely monitor these estimates to
ensure that flip-flop is not occurring.

Rik raises a good point, however.  So, as a first step, it might be good to
guard against flip-flop at the population level.  If that works and provides
sufficient stability so that flip-flop doesn't occur at the individual
level, then this might be an attractive parameterization because you can
still get a population estimate and IIV for ka directly.  If flip-flop is
still an issue at the individual level, then further constraining the model
at the individual level (ka>ke) might be considered and sacrifice (at least
directly) getting population estimates of ka and its IIV.

Ken
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From: Chuanpu Hu <chuanpu.2.hu@gsk.com>
Subject: RE: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/7/2003 3:08 PM


I agree with Ken's comments. Currently it is what I usually do. That is,
I watch the initial estimates so that flip-flop does not occur at the
population level, then I check it at the individual level. I actually
have had instances where flip-flop does occur at the individual level
although not at the population level (this answers part of Yanning's
question), and at that point I had to constrain KA>KE at the individual
level. Luckily, absorption half life wasn't the focus of that modeling.

Chuanpu 
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From: Nick Holford <n.holford@auckland.ac.nz>
Subject: Re: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/7/2003 4:14 PM

Hi,

There is a simpler method than constructing special parameterizations at
the population or individual level. It was mentioned earlier in this thread
but was not discussed ie. use of an EXIT statement

CL=THETA(cl)*EXP(ETA(cl))
V=THETA(v)*EXP(ETA(v))
K=CL/V
KA=THETA(ka)*EXP(ETA(ka))

IF (KA.LE.K) EXIT 1 101 ; try again (PREDERR message error code 101)

This is really no different than using the NOABORT option and letting NONMEM
catch instances of CL, V, F etc that are <=0. It is of course implicitly modifying
the distributions of CL,V,KA in some way to ensure KA>K but should we care about
this? The only situation that comes to mind would be if one tried to simulate from
the parameter estimates. But in any case I would probably want to truncate the
simulated parameters in the same way to avoid flip-flop.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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From: Yaning Wang <yaning@ufl.edu>
Subject: Re: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/7/2003 6:17 PM

Dear all:

Why do we have to constrain Ka>Ke on the individual level? When we
constrain TVKa>TVKe and find some individuals with Ka<Ke, isn't it
possible that Ka<Ke is the truth for those individuals, e.g. slower
absorption caused by food or other potential covariates?

Yaning Wang
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From: Justin Wilkins <jwilkins@uctgsh1.uct.ac.za>
Subject: RE: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/8/2003 2:54 AM

Hi all,

This is indeed the case with some of my subjects - some *are* slow
absorbers and their early individual predictions are too high if I
constraibn Ka < Ke.

Justin
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From: Ken Kowalski <Ken.Kowalski@pfizer.com>
Subject: RE: [NMusers] TVKa>TVKe or Ka>Ke?
Date: 8/8/2003 8:16 AM

Justin,

If this is the case, given that there is approximately a 10-fold difference
in your estimates of TVKa and TVKe, you must be getting an extremely large
estimate for the IIV of Ka in order for some individuals' Ka to be smaller
than Ke.  For those individuals where Ka < Ke what is the value of Ke?  If
it is considerably larger and closer to the population estimate of Ka (TVKa)
then I would still be suspicious that you're getting flip-flop.  On the
other hand, if the individual estimate of Ke is closer to the population
mean estimate of Ke (TVKe) and for some individuals the Ka just happens to
be even lower (ie., both Ka and Ke are small but Ka<Ke) then I would
probably agree with you that they are indeed slow absorbers.  If you truly
have a sub-population of slow absorbers, a histogram of the etas for Ka
should be skewed and/or bi-modal.  In this case I would investigate
covariates (e.g., food) that might influence Ka or consider a mixture model.

Ken
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From: Rik Shoemaker <RS@chdr.nl>
Subject: Re: [NMusers] Ka>Ke?
Date: 8/11/2003 4:06 AM

Dear Nick,

This sounds like a very good idea to me and solves my problem of obtaining
estimates of not very usefull parameters. I'll certainly try it when the
need arises. Thanks!

I'm personally not that worried about Ka>Ke for some and the reverse for
others; the point of the flip flop -as far as I understand- is that your
curves are not capable of telling you if one is larger than the other (equally
good fits can be obtained by reversing the two) and therefore the choice is
almost arbitrary (at least not data driven, but rather driven by what you think
your drug behaves like). If you do get better fits if you have reversal on the individual
level, I would indeed assume there is something else going on...

Rik
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From:  Ken Kowalski <Ken.Kowalski@pfizer.com>
Subject: RE: [NMusers] Ka>Ke?
Date: 8/11/2003 8:52 AM

Rik,

I would agree with you that in terms of individual fits it doesn't really
matter as you can always switch the parameters to get the identical fit.
But I don't think that's true at the population level.  For the FOCE method
the estimates of the etas are also flipped and that's got to impact the
approximation/estimation.  Another way to look at it is suppose that you
were doing a standard two-stage approach and a couple of your individual
fits had flip-flop parameter estimates.  You would want to reverse them
before you averaged across the individuals to obtain the population
estimates.

Ken
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From: Rik Shoemaker <RS@chdr.nl>
Subject: RE: [NMusers] Ka>Ke?
Date: 8/11/2003 8:58 AM

Ken,

Exactly! Which is why I would want the inequality to hold at both the
individual and the population level and not really allow individuals to
flip relative to the population estimates (as Justin Wilkins
suggested he required).

Rik
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From: Serge Guzy <GUZY@xoma.com>
Subject: RE: [NMusers] Ka>Ke?
Date: 8/11/2003 12:44 PM

If you would use simulations to test how your population PK software is
working, flip-flop will cause a bias in the final population estimates
you will obtain. The final population distribution will not be similar
to the one you began with and will depend heavily on the initial
estimates you begin with. Flip-flop can cause also your final population
not to follow normality (or log-normality) and bimodality is common when
not taking account for potential flip-flop.  Constraints (not
acceptance-rejection but rather the one proposed in this forum) are
therefore necessary to remove dependence between initial estimates and
final estimates and at the same time performing a valid population
analysis.  
Serge
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