- On 22 Mar 2003 at 21:49:19, jaya gudu (jsgundu.-at-.yahoo.com) sent the message

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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 - On 24 Mar 2003 at 06:56:48, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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> 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/ - On 23 Mar 2003 at 13:02:12, "Takimoto, Chris" (ctakimot.-at-.idd.org) sent the message

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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 - On 23 Mar 2003 at 16:21:43, "Takimoto, Chris" (ctakimot.aaa.idd.org) sent the message

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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 - On 24 Mar 2003 at 01:43:42, Laszlo Endrenyi (l.endrenyi.aaa.utoronto.ca) sent the message

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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 - On 24 Mar 2003 at 08:51:43, Michael.D.Karol.-a-.abbott.com sent the message

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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 - On 24 Mar 2003 at 23:51:15, Roger Jelliffe (jelliffe.aaa.usc.edu) sent the message

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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 - On 26 Mar 2003 at 09:30:13, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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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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