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The following message was posted to: PharmPK
dear all, i have seen in some papers (mostly in the
dose escalation studies), harmonic mean and pseudo
standard deviation were reported for T1/2, where as
mean and SD were reported for other parameters. can
any on tell me, under what circumstances this harmonic
mean and pseudo standard deviation be used, what does
they signify and why they are used for only T1/2.
thanks with regards
jayasagar gundu
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The following message was posted to: PharmPK
> dear all, i have seen in some papers (mostly in the
> dose escalation studies), harmonic mean and pseudo
> standard deviation were reported for T1/2, where as
> mean and SD were reported for other parameters.
The idea of reporting the harmonic mean for T1/2 is based on the
hypothesis that the distribution of the corresponding rate constant
(ln(2)/T1/2) has some known distribution. This is typically done prior
to use of a statistical hypothesis test e.g. Student's t-test, which
assumes a specific distribution.
IMHO there is no a priori known distribution for any PK parameter.
Given that all PK parameters are usually considered to be positive it
is clear that they cannot arise from a normal distribution. A log
normal distribution is a better candidate although clearly not perfect
because is allows infinitely small and large positive values. I prefer
to assume a log-normal distribution for hypothesis testing on PK
parameters and therefore the geometric mean(x) and the standard
deviation of of ln(x) are the statistics of interest. This assumption
is recommended by most regulatory authorities when performing
hypothesis testing for bioequivalence.
> can
> any on tell me, under what circumstances this harmonic
> mean and pseudo standard deviation be used, what does
> they signify and why they are used for only T1/2.
The use of harmonic means and pseudo standard deviations may indicate
that the authors, reviewers and editors of the papers you are reading
are practitioners of pseudo-science. A more constructive intepretation
would be that the inverse transformation of the T1/2 values makes the
empirical distribution more closely resemble a normal distribution
which then would help to make the statistical hypothesis test more
believable.
A better overall solution which does not rely on making distributional
assumptions is to apply the randomization test (see
http://wfn.sourceforge.net/rtmethod.htm for NONMEM related applications
and a short bibliography).
Nick
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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The following message was posted to: PharmPK
The harmonic mean may be a better indicator of central tendency for
half-life because half-life is derived from the rate constant in most
analyses. As you well know, t1/2 = 0.692/k where k is the elimination
rate
constant. Because you are deriving a mean for an inverse parameter, the
harmonic mean may be a better approach. For a nice discussion of the
harmonic means, pseudostandard deviations and half-lives, see Lam, F.
C.,
Hung, C. T., and Perrier, D. G. Estimation of variance for harmonic mean
half-lives, J Pharm Sci. 74: 229-31., 1985. Also, Dr. Harold Boxenbaum
has
been kind enough to distribute a nifty Excel spreadsheet that will
easily
calculate harmonic means and pseudostandard deviations for any dataset.
He
was kind enough to offer this to the general public the last time this
topic
came up on the listserv.
Chris H. Takimoto, MD, PhD, FACP
Associate Professor
Division of Medical Oncology, Department of Medicine
University of Texas Health Science Center at San Antonio
Address:
Institute for Drug Development
Cancer Therapy and Research Center
7979 Wurzbach Road, Rm. Z415
San Antonio, TX 78229
(210) 562-1725, Fax: (210) 692-7502
Email: ctakimot.-at-.idd.org
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The following message was posted to: PharmPK
For a very readable review of log-normal distributions throughout
science
and not just in medicine and pharmacology see the article by Limpert,
Stahel
and Abbt, Log-normal distributions across the sciences: Keys and clues.
BioScience 2001;51(5):341-52. It is largely supportive of Dr. Holford's
position that we should be making greater use of geometric means and
multiplicative standard deviations as summary statistics.
Chris H. Takimoto, MD, PhD, FACP
Associate Professor
Division of Medical Oncology, Department of Medicine
University of Texas Health Science Center at San Antonio
Address:
Institute for Drug Development
Cancer Therapy and Research Center
7979 Wurzbach Road, Rm. Z415
San Antonio, TX 78229
(210) 562-1725, Fax: (210) 692-7502
Email: ctakimot.-a-.idd.org
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The following message was posted to: PharmPK
I share Nick Holford's preference for assuming lognormal distribution
for pharmacokinetic parameters. In the case of T1/2, another benefit is
that the same conclusions are reached from the analyses of T1/2 and the
corresponding rate constant. E.g., the Geom.mean of T1/2 =
ln2/[Geom.mean of k] . Confidence intervals will also correspond and
tests of significance will be identical.
Laszlo Endrenyi
University of Toronto
Department of Pharmacology
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Jaya:
You might find the following publication helpful in answering your
question.
Denise J. Roe and Michael D. Karol, Averaging Pharmacokinetic Parameter
Estimates From Experimental Studies: Statistical Theory and
Application, Journal of Pharmaceutical Sciences, 86(5): 621-624 (1997).
Michael
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Dear Laszlo and Nick:
I don't understand why one should assume any particular shape
of the parameter distribution in a population. People have genetic
polymorphism, and may often have subpopulations of parameter
distributions. Nonparametric (NP) population modeling deals with this
problem, and it is not necessary to assume any particular shape for the
parameter distribution. Its shape is determined only by the data and by
the assay error pattern and the environmental noise pattern. Further,
NP pop modeling methods have consistent behavior, as the likelihood
function is exact, not approximated, as it is in most parametric pop
modeling software. such as that which uses FO or FOCE approximations to
get the likelihood.
Bob Leary has done a very thoughtful study comparing the
consistency, efficiency, and stochastic convergence properties of the
NP and the FOCE parametric methods. He presented it last year at the
PAGE meeting in Paris. His slides are on our web site for all to see,
if you click on "New Advances in Population Modeling". He shows that
even when the parameter distributions are truly Gaussian, that the
behavior using the FOCE approximation is not consistent or efficient,
while that of the NP method is. This means that even when the
distributions are truly Gaussian, that the means and variances and
correlations are of better quality when the NP methods are used. Very
interesting. So why should one assume any particular shape for
parameter distributions?
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine,
Division of Geriatric Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.-a-.usc.edu
Our web site= http://www.lapk.org
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The following message was posted to: PharmPK
Roger,
Roger Jelliffe wrote:
>
> PharmPK - Discussions about Pharmacokinetics
> Pharmacodynamics and related topics
>
> Dear Laszlo and Nick:
>
> I don't understand why one should assume any particular shape
> of the parameter distribution in a population.
People who want to do *HYPOTHESIS TESTING*, e.g. is the half-life in
group A different from that in Group B, will typically want to assume a
distribution. As I mentioned in my previous posting this is not
completely necessary because randomization test procedures can be used
for hypothesis testing without making distribution assumptions.
However, parametric methods are usually more convenient.
For *DESCRIPTION* of a parameter then one may be interested in more
than parametric statistics.
Nick
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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