- On 20 Dec 2004 at 12:22:46, "Gordi, Toufigh" (Toufigh.Gordi.aaa.cvt.com) sent the message

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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] - On 20 Dec 2004 at 14:19:30, Roger Jelliffe (jelliffe.at.usc.edu) sent the message

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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 - On 21 Dec 2004 at 11:42:45, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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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/ - On 20 Dec 2004 at 16:05:06, "Gordi, Toufigh" (Toufigh.Gordi.-a-.cvt.com) sent the message

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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 - On 21 Dec 2004 at 16:33:47, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

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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/ - On 20 Dec 2004 at 21:10:39, "Gordi, Toufigh" (Toufigh.Gordi.-at-.cvt.com) sent the message

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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 - On 21 Dec 2004 at 19:33:25, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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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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