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Everyone,
I need your collective wisdom on a PK issue. I understand the
statistical comparison's made during a bioequivalence study for one
drug. However, my question relates to the relevance and rational to
test two different drugs' concentrations statistically and determine
if there is a difference at each of the time points. Has this type of
statistical comparison ever been done in the past and published and if
so what was the context?
Let me provide an example:
Drug A (Concentration X, fixed volume) with time points at 0.5, 2, 12,
24 h
Drug B (Concentration 2X, same fixed volume) with time points at 0.5,
2, 12, 24 h
Statistically test each time point (0.5, 2, 12, 24 h) to determine if
Drug A is statistically higher in concentration at each time point to
Drug B. I know it can be done but what I am having trouble with is
the relevance of the analysis and the rationale to why you would want
to do such a measure. Also, if there are any other alternatives to
this method of assessing differences then I'd like to hear them.
I'd also like to hear from you whether you agree that this is a
kinetically relevant comparison or not. (call it a simple poll)
Best Regards,
Chris
Christopher S. Crean, MSc
Senior Manager, Drug Evaluation
Inspire Pharmaceuticals, Inc.
4422 Emperor Blvd., Suite 200
Durham, NC 27703
ccrean.-a-.inspirepharm.com
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The following message was posted to: PharmPK
You can compare the full model vs. the reduced model. The full model
assumes potential difference in the PK model parameters of both drugs.
The reduced model pools the data from both drugs and assumes they share
the same model parameters. You fit both model to your data and then
compare both objective functions. The Chi-square distribution with n
degrees of freedom (n being equal to the additional number of parameters
used in the full model)to see if there is a statistical difference.
This indeed would test only if there is an overall difference in the
Concentration time profile of both drugs.
Serge Guzy
President, CEO POP-PHARM Inc.
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Are these drugs structural homologs or a prodrug of another having
same pharmacological activity?
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Dear Chris,
This problem is a paired t-test (one-tail).
If the concentration data can be modelled, this is tranformed to
a kinetic problem. t-test, ANOVA, Wilcoxon signed-rank test and chi-2
test are used for kinetic parameters comparision.
I hope this helps.
Guangli
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The following message was posted to: PharmPK
Chris,
> However, my question relates to the relevance and rational to
> test two different drugs' concentrations statistically and determine
> if there is a difference at each of the time points. Has this type
of
> statistical comparison ever been done in the past and published and
if
> so what was the context?
The concentrations are highly correlated within individuals. There is
no pharmacokinetic rationale for doing multiple comparisons of
concentrations. Even if you did multiple comparisons and used a
correction such as Bonferroni it would be hard to do this properly
because the usual assumption is that the measurements from time to
time are independent. Indepednence is only plausible for the random
residual error but not true for the random differences between
individuals in the sample.
Has this been done before? Yes - I expect its been done but it makes
no sense to do it.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
n.holford.at.auckland.ac.nz
www.health.auckland.ac.nz/pharmacology/staff/nholford
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Dear Chris,
I am sorry that when I was thinking about metrics to compare two
vectors, I replied this post...
t-test is not for this question.
If your target is pharmacological purpose, comparision of PK
parameters derived from concentrion data is appropriate.
If your target is dosage form design, comparision of parameters
derived from data and comparision of data points directly are both
useful.
Guangli
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The following message was posted to: PharmPK
Hello Chris,
Luis Periera, recently in his article "Bioequivalence testing by
Statistical Shape Analysis" JPP August 2007, Vol34 No4 published an
approach for calculating bioequivalence by comparing distribution of
samples at individual time points. He uses Kullback-Liebler
Information Criterion to test the difference in sampling distributions
of test and reference formulation. The design issue is that time
points are to be same for both test and reference compounds. The
relevance of this analysis has been very well advacated in this
article.
More so often in destructive sampling a distribution may be assumed
at each time point and time weighted trapezoids are used to compare
bioequivalence between treated and untreated group. look at
"Establishing Bioequivalence in Serial Sacrifice Designs" JPP feb 2007
Vol34 no1.
Hope it helps
Varun Goel,
Graduate Student, Pharmacometrics
Department of Experimental and Clinical Pharmacology3
University of Minnesota
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Dear all,
We published a criterion which can be used to compare two time profiles:
Durisova, M., Dedik, L. Modeling in frequency domain used for
assessment of in vivo dissolution profile. Pharm Res, 14, 1997,
860-864,
Dedik, L., Durisova, M. System-approach methods for modeling and
testing similarity of in vitro dissolutions of drug dosage
formulations. Compt Meth Programs in Biomed, 69, 2002, 49-55.
Both studies are available for free at
www page:
http://www.uef.sav.sk/advanced.htm
[Accesesd: 2007, November 22].
Best regards,
Maria Durisova
www page:
http://www.uef.sav.sk/durisova.htm
[Accesesd: 2007, November 22].
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The following message was posted to: PharmPK
What you are describing is a repeated measures analysis of variance.
I don't know for sure but I suspect it will have similar power at
detecting treatment differences as comparing the AUCs, which can be
thought of as weighted means.
pete bonate
--
Peter Bonate, PhD, FCP
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Chris,
The problem you pose is, using an old aphorism, 'an old wine in a new
bottle'. In early '90 it was discussed in dept in the context of BE
studies: Is it not better to compare the SIMILARITY of the shapes of
concentrations/time profiles of Test and Reference drug products
rather than that of the absorption rate and extent?
Some seminal papers were published dealing with direct curve
comparison metrics. Furthermore, during Bio-International '94 a new
definition was proposed as a more appropriate to the very nature of BE
studies: "Two medicinal products are considered bioequivalent if their
concentration/time profiles are so similar that they are unlikely to
produce clinically relevant differences in therapeutic and/or adverse
effects".
I recommend the following few articles:
1. Steinijans, VW. et al. Metrics to characterize concentratioon-time
profiles in single- and multiple-dose bioequivalence studies. Drug
Inform J, 29, 981-987, 1995
2. Marston, SA. and JE. Polli. Evaluation of direct curve comparison
metrics applied to phramacokinetic profiles and relative
bioavailability and bioequivalence. Pharm Res, 14, 1363-1369, 1997
3. Mauger, DT. and VM. Chinchilli. An alternative index for assessing
profile similarity in bioequivalencr trials. Stat Med, 19, 2855-2866,
2000.
I hope this info will be of help to you.
Best regards,
Dimiter Terziivanov
--
Dimiter Terziivanov, MD,PhD,DSc, Professor and
Head, Clinic of Clinical Pharmacology and Pharmacokinetics,
Univ Hosp "St. Ivan Rilski",
15 Acad. Ivan Geshov st, 1431 Sofia, Bulgaria
e-mail: dterziivanov.-at-.rilski.com; terziiv.-a-.yahoo.com
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