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Hi All, I have concetration-time data for a biologic-like that spans approximately 1000 hours. There
are 5 analytes including metabolites which are quantifiable from 24 to 1000 hours. Concentrations
also have a broad spread so I am plotting them on a log scale. To me it makes sense to plot time on
X-axis on a log scale, however, this is unconventional. I am wondering if there is some other way
or some combination eg inset plots that are able to show data like this nicely.
Any suggestions, references will be welcome. I don't think I can do attachments here else I would
have attached an example.
Ahsan
--
Ahsan Naqi Rizwan
ahsannaqi.-at-.gmail.com
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From my point of view it MAY be OK if you also show everything on a linear scale also. There so many
illusions that the eye thinks it sees from looking at plots that the only thing I really trust is
the linear scale. But try it and see what it looks like. Remember that the eyeball fixes on bends in
lines, and the mind classifies based on those eyeball fixes, all too often. I am writing an
introduction for a book that discusses several of these illusions.
Best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D., F.C.P., F.A.A.C.S.
Professor of Medicine Emeritus,
USC School of Medicine
Founder and Director Emeritus
Laboratory of Applied Pharmacokinetics and Bioinformatics
Consultant in Infectious Diseases,
Children’s Hospital of Los Angeles
4640 Hollywood Blvd, MS #30
Los Angeles CA 90027
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Ahsan:
I have used square root of time (i.e. t^1/2).
William R. Wolowich, Pharm.D., R.Ph.
Assistant Professor
Department of Pharmacy Practice
College of Pharmacy
Nova Southeastern University
Ft. Lauderdale, Florida, USA
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Dear Ahsan:
in my opinion any approach is acceptable as long as it conveys the message and your analysis is not
introducing bias. Having said that this is what I would have done just plot X-axis on normal scale,
not to strain the eyes too much use a plotting program (e.g. origin?) that lets you introduce axis
break. Unfortunately most of the recent versions of plotting soiftware gotten away from this nice
tool called axis break.
Hope my suggestion helps your work.
Prasad NV Tata, Ph.D., FCP
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A common phenomenon approach is "if you want to minimize differences in plasma conc. vs. time
curves between the test and reference formulations then use log scale (semilog scale would be OK)
for concentrations."
"If you want to show the real differences between the formulations, then use the concentrations in
linear scale. Personally I would use the linear scale to display the entire conc vs. time curve."
Semi-logarithmic curves are useful to show differences in elimination half lives.
To be on the safe side, use both the linear and semi-logarithmic concentrations vs time curves.
Regards and best wishes.
Aziz
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Hello Dr Prasad,
We use this , axis break function regularly, in GraphPad Prism.
Hope it will help.
Regards,
Mitul Patel
[Also DeltaGraph - db]
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Yes. Log scale on any axis almost always makes things look better visually as it minimizes the
visual differences. That is a great way to lie with plots.
All the best,
Roger Jelliffe
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Sometimes log plots reveal truth that otherwise is hidden by plotting in
normal coordinates. Original scale plots and log plots are complimentary
in a sense as they allow to magnify high (original scale) or low (log
scale) ranges of values. Both types are useful, depending on what is
needed. Plots do not lie :) (if used correctly).
Leonid
--
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
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From: Masaki Hiraoka
Comparing a table containing time and concentration data with a figure
plotting the conc.-time data, one would see much more in the figure than
the table. Are these true?
Thus we study M&S not to tell lies.
Regards,
Masaki
--
From: Roger Jelliffe
Dear Leonid:
Don't be too sure. Even without obvious intent to deceive, they can carry powerful optical
illusions. How are the so-called "therapeutic ranges" of serum drug concentrations arrived at?
Best,
Roger
--
From: Martin Wahl
I am teaching my students: if there is more than one order of magnitude
on an axis, use log-scale, otherwise lin-scale is preferential. This is
also true for time scaling on the x-axis. Assuming timepoints like 0.5
h, 1 h, 1.5 h, 2 h, 12 h, 24 h, 72 h, in a lin-scale the "looking" of
the curve would be very much influenced by the late values. Here a
log-scale would help to have the short time values more prominently
displayed. A gap would in my eyes not be a good solution because one
would need several of them.
Martin
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Dear Masaki:
What you see and what you think you see can often be two quite different things. For
example, if you have two horizontal lines of equal length, but one has diagonal lines from the ends
pointing inwards at a 45 deg angle, and the other has similar lines from the end but pointing
outwards, which line appears longer? This is very common optical illusion. Do you know why this is?
There was a Russian mathematician who visited the lab of Dr. Richard Bellman at USC in 1966
who gave a talk specifically about this stuff, as he was interested in where the eyeball fixed when
you gave someone simple geometrical figures to look at.
He showed that it is because the eyeball fixes at bends in lines or at the inside of angles,
to place the area of macular vision where it can extract the most information from the figure. In
the first case, the eye fixes inside the ends of the horizontal line having the diagonal line
pointing inwards (inside the angle), but outside the ends of the line having the other lines
pointing outwards (but still inside the angles). The brain uses the proprioceptive information of
the eyeball fixes as the initial measure of the length of each line. From this comes the illusion,
he said, and I believe he was right.
There are really good books written on the value of well designed plots, and of the
misinformation that can also be conveyed with plots. I remember such a book, but cannot give the
reference for it. I will never forget that seminar by the Russian mathematician, whose name I
unfortunately never got.
All the best,
Roger
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Roger,
I believe the book you may be referring to is "The Visual Display of Quantitative Information" by
Edward R. Tufte.
Doug Smith
Tucson, AZ
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Dear Roger:
Thank you for the interesting story. I see you are saying something more
than optical illusions: The brain would see as what it wants/expects to see.
Dear Doug:
Thanks. I read a couple of reviews of "The Visual Display of
Quantitative Information" by Edward R. Tufte.
And I found this book very interesting.
Regards,
Masaki
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Hi everybody,
My two cents to the discussion. I would say that plotting the data on x-axis (time) on a log scale
is a bit problematic for the brain to cope with. I think that in PK one would treat time as a linear
process and that's how it should be expressed. Concerning the y-axis (concentration) to me is a
question of what is the claim. If I'm reading a paper suggesting 2- or 3-compartment model (IV
administration), I like to see the curve on a log scale to get an idea how the authors arrived to
that conclusion. Similarly, log data on a graph gives me a better idea of the absorption (non-IV
data). Log scale also makes it easier to see deviations from linear kinetics, such as saturations
etc. Personally I'd like to see the data given on a linear scale as a table, because you can give
more precise information that way (Mean, SD, SEM, range etc.). Those values are very difficult to
quantify from a graph and you are often left with an impression rather than cold data.
About illusions. I agree. Sometimes I feel like even the random selection of symbols by the Excel
emphasizes certain data sets.
Best,
Stefan
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From: William Wolowich
I think you are all missing the original intent of the question, i.e. how can one better visualize
a C Vs time plot when the time of interest extends from 0 to 1000 h, and at the same time keep the
detail in the early time points. The Ln time plot achieves this, as does the t^1/2 plot. Of course
one must carefully label the transformed axis to prevent misinterpretation. One of my pet peeves is
having someone throw a graph on the screen without introduction. "This is a plot of ...."
Wolowich
College of Pharmacy
Nova Southeastern University
--
From: Roger Jelliffe
That's the book I was trying to remember. Such a good book! Look at the graphic display of
Napoleon's march to Moscow and back! Look at the display of the train schedules between Paris and
Lyon, for example. Such good graphical display of the data!
And the eye is always drawn to bends in lines. Then the brain makes an evaluation of what we
think we see.
All the best,
Roger
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From: Roger Jelliffe
Thank you, William:
You are quite correct. I think it is difficult to know what best to do. The other option is
to break up the time axis into regions. Yes, both the ln time and sqrt time plots do this, and the
problem of course is that the eye can easily misinterpret what is sees.
Best to all,
Roger
--
From: Fabrice Nollevaux
Dear Stefan,
When you mention the usefulness of a table of the data in the linear scale "because you can give
more precise information that way (Mean, SD, SEM, range etc.)", I hope you have in mind data that
can reasonably be assumed as normally distributed?
Otherwise, statistics such as mean, SD or SEM are meaningless, and can even lead to wrong (ie quite
biased) interpretations.
I am always amazed of the number of official documents and publications presenting, comparing and
discussing parameters like Cmax, AUC or CL in terms of Mean ± SD, even when the distribution of
these parameters is known to be right-skewed, which is expected in the most common situations.
Regards,
Fabrice
--
From: Edward O'Connor
One great learning experience was with Heinz Valtin. No graphic could be presented without his
requirement, often interrupting the presentation, of explaining the abscissa and ordinate and why
they were presented in the way chosen.
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Dear Fabrice,
Thank you for pointing that out. I always send my graphs without error bars, hoping to get them
accepted as such. However, some reviewers are adamant to have them. That's when you have to deal
with your integrity.
Anyway, what I wanted to say was that even if only the mean is given, you will get the true
numerical value of it in a table, which you seldom get from a graph (resolution is too low). If you
also get things like the median and range, you know more about the results than you would looking at
the graph.
Best regards,
Stefan
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From: Roger Jelliffe
Dear Fabrice:
You are quite correct. Whatever the shape of the distribution is, normal, right skewed, or
whatever, you will do best if you estimate not just a summary single parameter value like a mean,
SD, etc, but rather if you estimate the entire distribution itself. You will always get better
likelihoods because the distribution is not constrained to have some assumed shape, but instead
depends only on the data itself. Furthermore, if you have made a population pharmacokinetic model
this way, you will then be able to develop a specific dosage regimen which will hit a desired target
goal with maximum precision (minimum expected weighted squared error). If you use parametric models
you will never be able to do this, and actually the issue will never arise. This is because
parametric models can never evaluate the error in target goal attainment, as with them there is no
means to do so. You might consider looking at:
1. Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and
Nonparametric Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and
Two Monte Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
2. Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of
Outliers and Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling
and Simulation Package for R. Therap. Drug Monit. 34: 467-476, 2012.
3. Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
4. Jelliffe R, Schumitzky A, Bayard D, Leary R, Botnen A, Van Guilder M, Bustad A, and Neely
M: Human Genetic variation, Population Pharmacokinetic – Dynamic Models, Bayesian feedback control,
and Maximally precise Individualized drug dosage regimens. Current Pharmacogenomics and Personalized
Medicine, 7: 249-262, 2009.
Very best wishes,
Roger
--
From: Helmut Schutz
Dear Fabrice (and Stefan),
> I am always amazed of the number of official documents and publications presenting, comparing and
> discussing parameters like Cmax, AUC or CL in terms of Mean ± SD, even when the distribution of
> these parameters is known to be right-skewed, which is expected in the most common situations.
>
Full ACK. See the FDA's amazing example:
http://www.accessdata.fda.gov/drugsatfda_docs/nda/2013/204412Orig1s000CrossR.pdf
(page 12).
How I love arithmetic means ± SDs! If I take this drug must I be afraid
of a ~6% chance to have a concentration of -300 ng/mL [sic] at seven
hours? Is antimatter part of the formula? Dangerous stuff indeed.
If somebody insists on arithmetic means of concentrations, ask them:
why? And don't forget to post the answer here, please. I'm always eager
to learn.
Helmut
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Greetings all,
Although log-log plots of pharmacokinetic data are seldom employed, it makes sense when the data
span many decades [log cycles] of time. This approach has been used successfully in the past in the
graphical and mathematical analysis of radionuclide retention data in man and animals. I would refer
you to Kenneth Norwich's excellent paper on noncompartmental models of whole-body clearance of
tracers [Annals of Biomedical Engineering, 25: 421-439 (1997)] and to an array of publications by M.
E, Wise over several decades [e.g., in Mathematical Biosciences; Bulletin of Mathematical Biology;
and Journal of Pharmacokinetics and Biopharmaceutics].
Lawrence H. Block, Ph.D.
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