Back to the Top
Hi Folks,
I’m updating an SOP for Noncompartmental analysis and I’d like to optimise the process as much as
possible. I’ve seen some discussion about the selection of the correct interpolation method in
Phoenix WNL, and I was wondering what was more appropriate for biological drugs, “Linear/Log
Trapezoidal” or “Lin up/Log Down”. I understand that in principal they are similar, but I was
wondering what the differences were and what would be more appropriate for NCA of mAbs and peptides.
I asked Certara last week and they suggested that “Lin Up/Log Down” was more appropriate due to
hepatic recirculation; however, this is more of a small molecule characteristic. Any advice on this
matter would be great.
Thanks in advance,
John
Back to the Top
Sounds like a tempest in a teapot. What is the relationship between hepatic recirculation and either
procedure? I would like to know their reasoning. But I never use noncompartmental analysis either,
and I don't understand why others seem to like it. Can you tell me why it is so great? Nonparametric
population modeling with free Pmetrics (www.lapk.org) gives the most likely results given any data
set (better than parametric methods), and also permits maximally precise dosage regimens to be
developed from the models. Parametric methods cannot do either, as the parameter distributions are
assumed and defined by the specific equations whose parameters are actually what are estimated with
those methods.
Best regards to all,
Roger Jelliffe
Back to the Top
Hi Roger,
NCA is a regulatory requirement for preclinical and toxicokinetic studies, so it needs to be done,
regardless of whether there is a better option. While this may change in time, until then we're
stuck with it. As for the relationship bewteen hepatic recirculation and the choice of interpolation
method, I'm not sure; enlightenment on this issue is one of the reasons I asked.
Thanks,
John
Back to the Top
Dear John:
What model to select for trapezoidal rule was discussed somewhere in " Gabrielson and Weiner -
Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications", If I recall correct
Overall they don't make much difference, however if you are perfectionist and accurate to the core
Linear Up and Log Down is way to go. Hope you can find convincing explanation in the book if not
please send me a personal e-mail I will fishout the correct reference and send it to you. { in my
memory lane while writing an SOP we as a team spent good 1 week and arrived at this conclusion)
Kind regards.
Prasad NV Tata, Ph.D., FCP
5620 Clarks Fork Drive
Raleigh, NC 27616
[I'm curious about the differences between "Linear up - Log Down" and "Linear/Log Trapezoidal".
Aren't they both using the trapezoidal rule. I rather like the method of Purves (RD, Purves. (1992).
Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and
area-under-the-moment-curve (AUMC). Jpb, 20(3)(3), 211–226. http://doi.org/10.1007/bf01062525) and
include it in my program, Boomer. An older paper by Yeh and Kwan (Yeh, K. C., & Kwan, K. C. (1978).
A comparison of numerical integrating algorithmn by trapezoidal lagrange and spline approximation.
Journal of Pharmacokinetics, 6(1), 79–98) could also be useful - db]
Back to the Top
Here is the information on the specific methods as implement in Phoenix
(From the Phoenix WinNonlin Manual, pg 22-23):
Linear Log Trapezoidal. Uses the log trapezoidal rule (see AUC
calculation and interpolation formulas on page 40) to create points after
Cmax, or after C0 for IV bolus, if C0 > Cmax. Otherwise, the linear
trapezoidal rule is used. If Cmax is not unique, then the first maximum is
used.
Linear Trapezoidal Linear Interpolation. This is the default method
and recommended for Drug Effect Data (220). It uses the linear
trapezoidal rule (see AUC calculation and interpolation formulas on
page 40), which is applied to each pair of consecutive points in the
dataset that have non-missing values, and sums up these areas. If a
partial area is selected that has an endpoint which is not in the dataset,
then the Linear Trapezoidal Linear/Log Interpolation rule is used to
add a concentration value for that endpoint.
Linear Up Log Down. When the concentration data is increasing, the
linear trapezoidal rule is used to add points. When the concentration data
is decreasing, the logarithmic trapezoidal rule is used to add points.
Linear Trapezoidal Linear/Log Interpolation. This method is the same
as Linear Trapezoidal Linear Interpolation except when a partial area
is selected that has an endpoint which is not in the dataset. In that case,
Phoenix inserts a final concentration value using the Linear Trapezoidal
Linear Interpolation rule or the Linear Trapezoidal Linear/Log
Interpolation rule if the endpoint is after Cmax, or after C0 for IV bolus
models, if C0 > Cmax. If Cmax is not unique, then the first maximum is
used.
The "interpolation" methods simply provide different ways of interpolating
concentrations for partial area calculations for time ranges that are not
in the observed dataset. There are really only 2 trapezoidal methods:
linear or logarithmic. Linear is commonly used for increasing
concentrations because increases in drug levels do not follow exponential
curves. Logarithmic is commonly used for decreasing concentrations because
decreases in drug levels often follow exponential decline; however, linear
can be used for declining concentrations (and is required by some
regulatory agencies).
I hope that helps.
Nathan S. Teuscher, PhD
Vice President, Scientific Training
Principal Scientist, Pharmacometrics
Certara?
Implementing Translational Science
100 Overlook Center, Suite 101, Princeton, NJ 08540
Back to the Top
I must confess I would be very interested to see any (experimental)
case were the difference between a simple trapezoidal rule, a
logarithmic one or the mix between the two is really higher than the
uncertainty on the AUC due to
1) the small number of available points
and (even more important)
2) the experimental variability, especially in concentration
determinations...
I agree that, theoretically, if one has a single exponential, the
log-trapezoid may be preferred, but even for a two-exponentials, I'm
not sure approximation by an exponential would lead to better
results...
Back to the Top
Be careful about making assumptions regarding therapeutic antibodies, some undergo recycling whereby
the antibody-target are taken into cells, the target dissociated from the antibody and the antibody
cycled back into circulation
--
Edward F. O'Connor
Back to the Top
So Lin up/Log down is probably more informative than lin/log trapezoidal as it can react to
recirculation...
[That's clever if correct. Maybe some 'proper' modeling would help - db]
Back to the Top
Check the shape of the PK profiles before making a judgement on “Linear/Log Trapezoidal” or “Lin
up/Log Down”. There are biologics which show completely conventional mono- or biexponential
kinetics, such that “Lin up/Log Down” is appropriate. However, if the kinetics are nonlinear due to
target mediated drug disposition (TMDD), the shape can change such that linear on both sides would
be more appropriate.
However, one should also be aware that interpreting the results of NCA is fraught with problems for
nonlinear compounds such as many biologics, due to implicit assumptions of linearity. NCA is fine to
report AUC, Cmax, Tmax, i.e. check serum/plasma exposure, but that's about it. On half-life, which
one: alpha, beta, gamma or delta? Or after which dose or over which concentration range? (see
Peletier & Gabrielsson JPKPD 2012 39 429-51). Using ratios of AUC to calculate, for example, BAV can
give marked errors (Hayashi 2001 Eu J Pharm Sci 13 151). Deriving parameters such as volumes can
also be incorrect. Quoting Lobo Hansen & Balthasar (2004 J Pharm Sci 93 2645)
"Contrary to these expectations, in most reports
of antibody pharmacokinetics, antibody Vss has
been reported to be small (i.e., approximately
equal to the plasma volume of the study subject)
and concentration-independent (e.g., Table 1).
However, it is worth noting that the vast majority
of pharmacokinetic analyzes of antibody drugs
(and of drugs in general) have estimated Vss via
noncompartmental, moment approaches or via
computer fitting with mammillary compartmental
models (e.g., the 2-compartment open model, etc.).
These analytical approaches are based on the
assumption that the site of antibody elimination
is in rapid equilibrium with plasma (i.e., it is
assumed that all elimination is from the ‘‘central’’
compartment). This assumption may be valid for
many antibodies, but incorrect for others (e.g.,
antibodies that bind to and internalize within cells
in tissue sites). It is known that antibodies are
catabolized in tissues throughout the body, including
sites where the rate of antibody distribution is
likely to be relatively slow. In the extreme case,
where the rate of distribution of antibody from
tissue to blood is much slower that the rate of
antibody catabolism in tissue sites, Vss will be
inappropriately inferred to be equal to the plasma
volume (i.e., independent of the relationship of
mass of antibody in the body to the concentration of
antibody in plasma)."
Best advice - talk to the modellers in your own company. You have some very good ones.
All the best, Phil
Philip J Lowe PhD
Executive Director Pharmacometrics Scientist
Novartis Pharma AG
4056 Basel, Switzerland
Back to the Top
We'll go with the Linear Up Log Down calculation method then. Thanks for all the replies.
Cheers,
John
| PharmPK Discussion List Archive Index page |
Copyright 1995-2014 David W. A. Bourne (david@boomer.org)