- On 24 Jun 2002 at 10:46:08, "He Ju Xiu" (hejuxiu.-at-.hotmail.com) sent the message

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Dear all,

I have a problem now. I carried out a pharmacokinetic study on 60

rats. The rats were orally administered with one drug, and they were

sacrificed for whole blood's sampling at the time intervals (10 time

points). Each time point contains 6 rats' plasma concentration data.

I would like to know how to determine the Cmax and Tmax and their

variance, since the individual Cmax and Tmax were not available.

Thanks. - On 24 Jun 2002 at 17:46:18, eoconnor.at.Therimmune.com sent the message

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If I understand this you have one sample at each point consisting of pooled

blood or pooled results from 6 rats. You can get a Cmax and Tmax but any

descriptive statistic of variance is lost since you have only one sample per

point. - On 24 Jun 2002 at 20:30:57, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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> The following message was posted to: PharmPK

>

> If I understand this you have one sample at each point consisting of pooled

> blood or pooled results from 6 rats. You can get a Cmax and Tmax but any

> descriptive statistic of variance is lost since you have only one sample per

> point.

>

This is not necessarily the case. Mixed effect models can come to the

rescue here e.g.

Hing JP, Woolfrey SG, Greenslade D, Wright PMC. Is mixed effects

modeling or naive pooled data analysis preferred for the

interpretation of single sample per subject toxicokinetic data?

Journal of Pharmacokinetics & Biopharmaceutics 2001;28(2):193-210.

The basic idea is that you are prepared to assume some reasonable

value for the residual error (measurement error, etc) then a mixed

effect model can recover information about the between subject

variability in model parameters. You could then use these PK

parameters to simulate design dependent statistics (like Cmax and

Tmax) with multiple samples per rat and from that compute their

variability.

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

email:n.holford.-a-.auckland.ac.nz

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 25 Jun 2002 at 10:33:46, "He Ju Xiu" (hejuxiu.aaa.hotmail.com) sent the message

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I am sorry to make you misunderstand my problem. I did have six

samples (not pooled) at each point. The samples at different point

came from different rats. I have calculated the AUC and its variance

according to the Bailer's method. I tried but failed to find any

reference regarding estimating the Cmax and Tmax and their variance

in this kind of situation. - On 25 Jun 2002 at 10:34:19, daniel.martinez.-a-.beaufour-ipsen.com sent the message

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Hi Xiu,

I think the best way to have an approach of these two parameters is to take

each group of six rats and calculate their mean±sd plasma concentration

value. With this mean±sd plasma concentration data obtained you have both

Tmax and Cmax values. The standard deviation give you their variance.

>From my point of view the major problem in these cases is when we start to

study our drug and we don't know between what time the Cmax is achieved. We

should obtain the information from books or doing a pilot study and when we

know this, we should do an appropriate sampling schedule in order to obtain

a good approach of this parameter.

I hope it helps.

Daniel Martínez

RIA Laboratory

Metabolism & Pharmacokinetics Service

Research & Development Department

IPSEN PHARMA, S.A.

Ctra. Laureà Miró 395

Sant Feliu de Llobregat, Barcelona, Spain

daniel.martinez.-a-.beaufour-ipsen.com - On 25 Jun 2002 at 10:46:30, "McBurney, Alan" (McBurneA.aaa.ukorg.huntingdon.com) sent the message

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As part of our analysis of toxicology studies we routinely perform

statistical analysis of the above parameters using the following

methodology;

For each treatment group, in order to obtain estimates of areas under the

plasma concentration-time curves to 24 hours (AUC24), given that different

animals are used to obtain blood samples at each time point, the trapezoidal

approach is used on the mean values at each time point. Variances are also

obtained using standard statistical techniques (Bailer 1988) allowing

comparisons between groups to be carried out.

The means and their variances are dose adjusted to 1 mg/kg, and chi-square

tests for heterogeneity (Miller et al 1939) carried out between the

dose-adjusted estimates for the dose groups, a measure of dose

proportionality on each study day. Comparisons are made between the days

for each dose group separately using chi-square tests.

The plasma concentrations which give the maximum mean concentration were

used as estimates of Cmax. A logarithmic transformation is performed on the

data prior to analysis in order to stabilise the variances.

BAILER, A.J. (1988) Testing for the equality of area under the curves when

using destructive measurement techniques J. Pharmacokin. Biopharm., 16,

303-309.

MILLER, L.C., BLISS, C.I. and BRAUN, H.A. (1939) The assay of digitalis J.

Amer. Pharm. Ass. 28, 644-657.

HUNTINGDON LIFE.SCIENCES LIMITED

http://www.huntingdon.com

Huntingdon Life.Sciences Limited registered in England No. 1815730.

Registered office: Woolley Road, Alconbury, Huntingdon,

Cambridgeshire PE28 4HS - On 25 Jun 2002 at 14:58:53, eoconnor.aaa.Therimmune.com sent the message

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Then you have six rats per point, each of point is from a group of different

rats. This should work very well. - On 26 Jun 2002 at 21:08:27, "He Ju Xiu" (hejuxiu.aaa.hotmail.com) sent the message

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Thank you all for your kind suggestions. The followings are the raw

pharmacokinetic data I obtained from the 60 rats (6 rats were killed

for each time point). The maximum of the mean concentration is 1.014

É g/ml with standard deviation of 0.541 at 4 h. Shall I use these

values as the Cmax, SD of Cmax and Tmax (its variance is lost),

respectively? Any suggestion and reference is highly appreciated.

0 0.25 0.5 1 2 4 6 9 12 24 h

0.000 0.015 0.134 0.574 0.643 0.303 0.446 0.025 0.043 0.024

0.000 0.013 0.327 0.540 0.489 1.419 0.403 0.044 0.014 0.009

0.000 0.009 0.110 0.852 0.482 0.807 0.164 0.025 0.025 0.008

0.000 0.043 0.046 0.284 1.358 1.556 0.287 0.021 0.042 0.006

0.000 0.029 0.307 0.836 0.539 0.520 0.146 0.035 0.009 0.012

0.000 0.033 0.688 0.407 0.529 1.476 0.230 0.158 0.007 0.012 - On 27 Jun 2002 at 11:29:17, "McBurney, Alan" (McBurneA.-a-.ukorg.huntingdon.com) sent the message

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Go with the Cmax at 4 hours and the SD calculated. With a destructive

sampling study you are never going to be able to estimate the variability of

Tmax. You will only have a single sample per animal in your design.

Some rodent sampling designs will sample up to 3 time points per animal.

However, due to welfare considerations, these time points will be well

separated and would not be useful for determining the Tmax in the individual

animal.

Tmax must inevitably be derived from the mean data and hence no variability

can be determined.

Alan

HUNTINGDON LIFE.SCIENCES LIMITED

http://www.huntingdon.com - On 27 Jun 2002 at 12:42:42, eoconnor.-a-.Therimmune.com sent the message

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Why is it lost? you have the data - On 27 Jun 2002 at 15:12:32, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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"McBurney, Alan (by way of David Bourne)" wrote:

>

> Go with the Cmax at 4 hours and the SD calculated. With a destructive

> sampling study you are never going to be able to estimate the variability of

> Tmax. You will only have a single sample per animal in your design.

>

> Some rodent sampling designs will sample up to 3 time points per animal.

> However, due to welfare considerations, these time points will be well

> separated and would not be useful for determining the Tmax in the individual

> animal.

>

> Tmax must inevitably be derived from the mean data and hence no variability

> can be determined.

> Alan

>

> HUNTINGDON LIFE.SCIENCES LIMITED

>

> http://www.huntingdon.com

Never say never...

As I pointed out earlier it is quite feasible to estimate variability

in Tmax from destructive sampling data. It just requires you to

progress beyond the concepts of SHAM (SHape, Area, Moment)

pharmacokinetic analysis promoted by the Walt Disney School of

Pharmaceutical Science.

I wrote:

> > This is not necessarily the case. Mixed effect models can come to

>the rescue here e.g.

> > Hing JP, Woolfrey SG, Greenslade D, Wright PMC. Is mixed effects

>modeling or naive pooled

> > data analysis preferred for the interpretation of single sample

>per subject toxicokinetic

> > data? Journal of Pharmacokinetics & Biopharmaceutics 2001;28(2):193-210.

> >

> > The basic idea is that if you are prepared to assume some

>reasonable value for the residual

> > error (measurement error, etc) then a mixed effect model can

>recover information about

> > the between subject variability in model parameters. You could

>then use these PK

> > parameters to simulate design dependent statistics (like Cmax and

>Tmax) with multiple

> > samples per rat and from that compute their variability.

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

email:n.holford.-a-.auckland.ac.nz

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 4 Jul 2002 at 11:12:11, harry.mager.hm.-at-.bayer-ag.de sent the message

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To put my cent in ...

You may want to use a resampling procedure [H. Mager & G. Goeller, J. Pharm.

Sci. 87, 372-378 (1998); Mager, H. and G. Göller, Drug Information Journal 31,

551-562 (1997)]. This procedure can be applied to all functions of the

concentrations, not only to linear ones, as the Bailer approach is

restricted to

(although there are some modifications and approximative solutions for the

nonlinear case, e.g., lin-log AUC). It has been argued in this forum that the

industry has to rely on NCA analyses in toxicokinetics (in general) - both NCA

and compartmental analyses can be applied and all types of parameters

calculated.

The resampling procedure does not suffer from the disadvantage of more or less

artificially "estimating" intra-individual variability, as it would

be necessary

with a mixed modeling approach. By the way, simulation results may be heavily

influenced by the particular values of those "guesses".

The NCA resampling approach applied to your data gives:

arithmetic means geometric means 5%

percentiles

95% percentiles

Cmax = 1.16 sd = 0.382 Cmax = 1.09 sd-geo = 1.47 Cmax = 0.54

Cmax = 1.48

tmax = 3 sd = 1.3 tmax = 2.6 sd-geo = 1.83 tmax = 1

tmax = 4

(distributions seem to be skewed).

Would you mind sending me your Bailer AUC results for comparison with

ours (dose

?).

Harry

Dr. Harry Mager

Head Biometry & Pharmacometry

Bayer AG

PH-PD-GCP Biometry & Pharmacometry

D-42096 Wuppertal / Bldg. 470

eMail: Harry.Mager.HM.aaa.Bayer-AG.de

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