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Dear all,
I have a general question, which I'll try to describe by a somewhat
specific example. Let's say that we want to investigate whether renal
function affects the clearance of a compound. One way would be to do a
study, where subjects are divided into 4 groups of normal, mild,
moderate, and severe renal impairment depending on their creatinine CL
values. Then we can test for differences between the groups and get
some p-values. I am not suggesting that this is the way to go. The
point is that we can estimate how many subjects we need to be included
in such a study to be able to draw a conclusion with a certain power
and confidence. Let's say that in our hypothetical study we need 25
subjects in each renal function group to give us enough power to detect
differences.
Since I think of modeling as soon as I see an observation vs. time
graph, I am interested to set up a PK model using data from this study.
The question is changed: we are no longer interested to compare
different groups, but want to establish a "global" relationship between
creatinine CL and the pharmacokinetics of our compound. Once you have
the relationship known and established, we don't need to worry about
classifying our subjects into various, and sometime arbitrary, groups
but can use their creatinine CL values to predict how the
concentration-time curve looks like in this subject.
My question is: how do we decide the number of subjects we need for
such approach? Will 100, equally dispersed over the 4 groups give us
enough information? What about 80 (4x20)? However, my guess is that we
don't need to estimate the number of subjects from a "classical"
statistical view (which suggests 4x25 in our example) in order to
estimate how many subjects we would need in our modeling approach. Any
thoughts?
Toufigh Gordi
P.s. I assume an equally important question would probably be: how do
you convince people that you have a good model if you do not offer a
p-value for differences between the groups?
[Doesn't this become a linear regression (or other model) for PK
parameter such as clearance or kel ;-) versus creatinine clearance -
db]
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Dear Toufigh:
Why do you classify by renal function? Why not simply examine
the regression relationship between Kel, for example, or clearance, and
CCr? I think you would have a much better quantitative relationship to
use. You can also have a nonrenal intercept if there is one.
Incidentally, you might look at Jelliffe R: Estimation of Creatinine
Clearance in Patients with Unstable Renal Function, without a Urine
Specimen. Am. J. Nephrology, 22: 3200-324, 2002.
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.aaa.usc.edu
Our web site= http://www.lapk.org
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The following message was posted to: PharmPK
Gordi,
Your question reflects the dichotomy of learning and confirming.
Confirming asks yes/no questions e.g. is CL different in renal
impairment? Learning asks how much questions e.g. what is the slope of
the line relating CL to creatinine clearance?
Confirming questions are answered by hypothesis testing e.g. t-test.
The design for confirming questions uses power as it's performance
metric. Design properties such as number of subjects, number of renal
function categories are chosen to achieve a target power.
Learning questions are answered by parameter estimation e.g. linear
regression. The design for learning questions typically uses bias and
imprecision as it's performance metric. Design properties such as
number of subjects, distribution of creatinine clearance are chosen to
achieve a target bias and imprecision (RMSE). In your case the how much
questions might include:
What is renal clearance?
What is the non-renal clearance?
What is the slope of the line relating renal clearance to creatinine
clearance?
plus between subject random effects on the clearances...
Confirming questions are usually applied to jump over regulatory
hurdles. Is it safe? Is it effective? Or to get published in p-value
journals (e.g. NEJM). Is P<0.05?
Learning questions are used by scientists to find out how the world
works. When you know how it works then you can usually find an easy way
to jump over the hurdles.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.at.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
Before there are more replies on my question on estimating the number of
subjects in a "modeling" study, let me make it clear that the renal
impairment example I presented was just that: an example. I am not
looking for any answer on how to analyze data from such study. The very
reasonable analysis would be to investigate whether there is a
correlation between different PK parameters and CLcr (as stated by Roger
and David).
The point with my question is to discuss how I can "sell" the different
approach, i.e. the learning study (as Nick puts it), to people used to
the confirmatory approach.
I am a firm believer of understanding the whole system (through a proper
study design and PK/PD modeling) in contrast to looking for a difference
between 2 or more groups. My problem is to convince people with no
modeling background, who only look at the p-value, to understand the
differences and advantages of the modeling approach over the other. To
do so, I need to come up with answers with regard to the number of
subjects in my proposed design compared to the confirmatory design,
where the statistician can relatively easily estimate the number of
subjects needed. I won't be much credible if I can't even tell how many
subjects I need to have in my study on the top of the fact that I don't
even try to show any differences between groups!
Sorry if my example created a confusion.
Toufigh
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The following message was posted to: PharmPK
Gordi,
You could try asking your P-value-oholic colleagues if they would
accept a design that was powered on the yes/no question that asked "Is
the slope of the line relating renal clearance to creatinine
clearance?" different from zero. You could then design your trial to
achieve sufficient power to answer this confirming question. The number
of subjects required could be determined by this method.
After the trial is analyzed you can then use the continuous learning
relationships to categorize covariate groups (e.g. mild, moderate,
severe) to invent something for the drug label. Your continuous model
would be able to be used to simulate the performance of the categorical
label statements.
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-at-.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
Dear Nick,
In this specific example of relationship between renal function
(estimated as CLcr) and CL or Vd of the compound, I have actually
managed to convince people to accept my modeling and do not be bothered
with what renal function group the subjects belong to :-). On the other
hand, we made sure in the protocol that an even number of subjects are
included in each group, thereby ensuring that we cover a wide range of
renal function values.
However, in other situations the relationship between, let's say
concentration and effect, might not be a simple linear regression. And
to me that's the whole idea with modeling, i.e. understand the system so
that its behavior can be predicted independent of whether it is a linear
or non-linear relationship. Let me create another (this time
hypothetical) example. The study team wants to see whether subjects
heavier than 100 kg have a different response to a certain drug. To
answer this question, they design a study where subjects heavier and
lighter than 100 kg are given the drug and some effect is measured.
Normally, they would put a restraint so that subjects are not much
lighter or heavier that 100, i.e. only subjects between 80 to 120 kg are
included. The statistician can calculate what number of subjects is
needed, e.g. 40 below and 40 above 100 kg, and later on generate a
p-value to statistically reject or not reject the null-hypothesis. My
point of view is that the whole question is wrong! I would rather see a
spread of subjects between, let's say, 60 to 140 kg. Once I know the
behavior of the system in this wide range, I can answer not only the
question of "what effect in subjects above 100 kg" but also any other
value within this range. To me it is much more informative. The
problems, however, are that I cannot generate a p-value and I am unable
to be specific in putting forward the number of subjects that should be
included in this study. One can, of course model the data from the study
as proposed by the study team and try to make some sense out of it.
However, where I want to disperse it more, the statistician would like
to concentrate in order to avoid "outliers".
Imagine if I come with an alternative design, where I want to include
subjects in a wider range and do not test for differences between >100
and <100. I am producing no p-value, and I cannot come up with a
rationale on how many subjects I'd like to include :-). It will be a
tough sell.
Toufigh
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The following message was posted to: PharmPK
Toufigh,
I think we are in full agreement. I understand your renal function
example is just intended to illustrate the principle of how difficult
it is to get P value oriented folks to take a look at reality. The
science of clinical trial simulation using PKPD and Disease Progress
models plus Covariate and Execution models is orientated around the
idea of describing and using our understanding of reality. If you can't
convince your statistician to wake up then maybe you should try beating
your head against a different wall :-)
Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)