- On 26 Aug 2015 at 08:57:50, Hood, John (hoodj.at.medimmune.com) sent the message

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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 - On 26 Aug 2015 at 10:24:54, Roger Jelliffe (jelliffe.-at-.usc.edu) sent the message

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 - On 27 Aug 2015 at 08:28:32, John Hood (hoodj.aaa.medimmune.com) sent the message

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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 - On 27 Aug 2015 at 08:37:45, Dr. Prasad Tata (drprasadtata.-a-.yahoo.com) sent the message

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] - On 27 Aug 2015 at 09:08:18, Nathan Teuscher (Nathan.Teuscher.-at-.certara.com) sent the message

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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 - On 27 Aug 2015 at 12:41:27, Emmanuel Curis (emmanuel.curis.-at-.parisdescartes.fr) sent the message

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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... - On 27 Aug 2015 at 13:44:58, Edward O'Connor (efoconnor.-a-.gmail.com) sent the message

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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 - On 28 Aug 2015 at 08:34:54, John Hood (hoodj.-at-.medimmune.com) sent the message

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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] - On 28 Aug 2015 at 08:36:16, Lowe, Phil (phil.lowe.-a-.novartis.com) sent the message

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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 - On 28 Aug 2015 at 08:37:11, John Hood (hoodj.at.medimmune.com) sent the message

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We'll go with the Linear Up Log Down calculation method then. Thanks for all the replies.

Cheers,

John

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