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Re: [NMusers] How to account for M-M in the presence of Ka>Ke constraint in PopPK model

From: Nick Holford <>
Date: Thu, 09 Jul 2015 09:13:08 +0200

Lei, Paulo,

There is no need to feel any pain due to "flip-flop" when elimination is
by a mixed order process. The "flip-flop" only causes difficulty in
assigning 'ka' and 'k' because of the symmetry of the sum of two
exponentials. If you have a mixed order process there is no 'k' and
therefore no symmetry of exponentials and therefore no "flip-flop".

Best wishes,


On 9/07/2015 7:57 a.m., Paolo Denti wrote:
> Dear Lei,
> I feel your pain, cuz I have also battled with models with stubborn
> flip-flop and I started concocting all sort of codes similar to yours
> to prevent it - you can probably find some desperate posts of mine
> about this on NMUSERS :).
> In my experience, the only code that sort of works without causing too
> many side-effects is the one that prevents flip-flop of the typical
> values (the THETAs). Unfortunately, this does not work every time, but
> all the other codes accounting for individual parameters (such as the
> one you propose) introduce funny correlations between the parameters
> and the ETAs, they reshape the between-subject variability, and they
> may end up causing more trouble than they solve.
> In your case with nonlinear clearance, it may be even more complicated
> than usual.
> In my experience, the best option is to use priors on ka and volume,
> even weakly informative. These should help stabilising your model.
> Adding priors may seem "artificial", but if you think about it, it is
> doing exactly what you are trying to achieve with all these tricky
> codes. One cannot solve the flip-flop problem only with data from oral
> administration, the only way is to add external information, like the
> fact that you expect ka to be larger than ke, or include IV data that
> helps you identify the correct value of volume. With the priors you do
> just that, and in a more natural way than "cheating" NONMEM with funny
> codes.
> Good luck!
> Paolo
> On 2015/07/08 22:41, Lei Diao wrote:
>> Dear NONMEM Users,
>> I have a popPK model for which the Ka is constrained to be larger
>> than Ke at the individual level to avoid flip-flop. The question is
>> that if there is an additional nonlinear clearance component (M-M),
>> how should I constrain between the absorption rate (KA) and terminal
>> phase elimination rate (KE) since nonlinear clearance causes the KE
>> to change with time? Is there any reference on this topic?
>> KA and KE constraining in the absence of nonlinear clearance in NM code:
>> KE=((K+K23+K32)-SQRT((K+K23+K32)*(K+K23+K32)-4*K*K32))/2
>> Thanks a lot for your input!
>> Lei Diao
>> Biogen
> --
> ------------------------------------------------
> Paolo Denti, PhD
> Pharmacometrics Group
> Division of Clinical Pharmacology
> Department of Medicine
> University of Cape Town
> K45 Old Main Building
> Groote Schuur Hospital
> Observatory, Cape Town
> 7925 South Africa
> phone: +27 21 404 7719
> fax: +27 21 448 1989
> ------------------------------------------------
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Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(7)80 48 55 50

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.
Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol. 2015;79(1):18-27.

Received on Thu Jul 09 2015 - 03:13:08 EDT

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