- On 9 Apr 2003 at 09:40:23, Rostam Namdari (chista90.aaa.yahoo.com) sent the message

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Dear Colleagues,

Generally, most PK parameters are log-normally

distributed including Cmax that is why there is a

tendency to report the Cmax of several subjects as

geometric mean. However, we believe plasma

concentrations are normally distributed continuous

variable and adequately characterized by arithmetic

mean. I see a little bit of controversy here. Would

some one please provide some explanation?

Rostam - On 9 Apr 2003 at 15:25:07, xia.luo.aaa.sepracor.com sent the message

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I often found plasma concentrations are log normally distributed.

Xia - On 9 Apr 2003 at 17:32:36, Rostam Namdari (chista90.-a-.yahoo.com) sent the message

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Thanks Xia, what statistical parameter do you use as a

measure for the center of a distribution for each time

point? Arithmetic mean, median, geometric mean?

Rostam - On 10 Apr 2003 at 13:55:44, xia.luo.aaa.sepracor.com sent the message

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Before the exploratory analysis, I would like to see how plasma

concentration distribution looks like. Usually, after log transform, the

distribution is very close to normal. This can be seen if using Q-Q

plot.

If log normally distributed, then geometric mean is a good statistics

for

center location. Please correct me, if I am wrong.

Thanks

Xia - On 11 Apr 2003 at 12:28:02, "paul&els" (meyvisch.at.pandora.be) sent the message

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Dear Rostam,

Under the (usually fair) assumption of log normality, the arithmetic

mean is a biased estimate for the center. Both median and geometric

mean are unbiased estimates for the center but the geometric mean is

more 'precise' (smaller variance) though less robust for outliers. The

geometric mean may seem to be the best choice but I do not favour using

the geometric mean in case some points may be 'zero-like' (e.g. below

the detection limit) since this complicates things. Hence I propose to

use the geometric mean and median for Cmax but take the median as

primary center statistic for the individual time points.

I did a small simulation exercise by drawing 10,000 samples from the

standard normal. Anti-logging this sample yields a lognormal

distribution with center 1.

I obtained :

Arithmetic mean = 1.642 (biased !)

Median=0.999 (unbiased)

Geometric mean=0.988 (unbiased)

There are a number of diagnostic tools to see if a sample is drawn from

a (log) normal distribution but I should not 'overdiagnose',

particularly not when the sample size is small.

Regards,

Paul Meyvisch

Statistician - On 11 Apr 2003 at 17:15:04, Rostam Namdari (chista90.-a-.yahoo.com) sent the message

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Dear Paul,

Thanks for your e-mail, very helpful indeed. But I

have never seen the average time-concentration profile

for group of patients express as median concentration

vs time. These data often presented as MeanąSD or SE

and I mean arithmetic mean. So, may be other s can

comment on this? How do regulators likes to see the

data presented?

On the same subject, Xia, suggested that usually,

after log transform, the distribution is very close to

normal. This can be seen if using Q-Q plot. I was

wondering why Q-Q plot and not normal probability

plot? Any comments?

Rostam - On 13 Apr 2003 at 15:51:56, Berber Snoeijer (bsnoeijer.-a-.biometricsupport.nl) sent the message

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Dear Rostam,

In my work for several CROs, we were in most cases used to present only

a

geometric mean curve. Statistics like 95% confidence interval, min, max

and

median for individual time points were calculated and only presented as

numbers. In some cases, sponsors required median curves and back

calculated

SDs.

Aritmethic means are not OK. Try it yourself: Put the arithmetic curve,

the

geometric curve and the median curve in one graph and you will see that

the

median curve and geometric curve are more or less equal while the

arithmetic

curve is clearly different. This is an indiciation that the data is

log-normally distributed. Also normal probability plots, will confirm

this.

As far as I know, regulators are used to see geometric mean curves. So,

I

would advice to create them.

Kind Regards

Berber Snoeijer

Netherlands - On 15 Apr 2003 at 12:22:44, Rostam Namdari (chista90.-at-.yahoo.com) sent the message

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Dear Willi,

In your textbook 'Parameters for Compartment-free

Pharmacokinetics' (Shaker Publishing House,

Aachen,Germany 1999) in Chapter 8, Table 8.1 you have

indicated the following values/statistics should be

reported for individual plasma conc at each time

point: arithmetic mean, SD, median, min and max.

Do you agree with recent discussion between Berber and

I that geometric mean should also be reported and

perhaps it is more relevant? I noted all the CROs that

I have worked with only report arithmetic mean ą SD

(not SE). Is this because most people are used to

arithmetic mean? Please comment. Thanks

Rostam

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