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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.
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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.
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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/
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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.
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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
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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
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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.
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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
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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
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Why is it lost? you have the data
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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/
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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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