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Dear all,
I have seen some discussions about handling values below LLOQ in PK
studies
during 1998 and 2002, but there is still some questions here that I
don't
quite understand.
When I get PK data in order to do PK modeling or estimate PK parameters
in
a phase I study, all concentration values below a certain value, LLOQ,
are
omitted and replaced by the information:laboratory
obtains a quantity it considers the concentration as not quantifiable
and
therefore prefers to keep the quantity as a secret. I do not quite
understand
the reason for this and wonder whether it is common. Does this happen
to all
of you, or are some of you so lucky that you get all the observed
analysis
results?
To me it seems strange first to throw some observed values away and
then try
to estimate them or replace them with some arbitrary numbers, which is
sometimes done. Why do we have a LLOQ and what is the problem with
values
below since they are not trusted? Is there an unacceptable deviation
between
the observed and the true concentration below LLOQ which is not present
above
LLOQ?
A deviation between an observed quantity and the true value can be due
to
random variation, expressed in a variance, and/or a systematic
variation,
expressed as a bias. The random variation is of course not a problem,
it is
just a question of using the right variance function in the model. It
makes
no sense to throw values away just because of a high coefficient of
variation.
Then why is LLOQ often defined as 10*sigma, where sigma is the standard
deviation of a blank?
That leaves the bias. But when a zero sample or blank is included among
the
samples it should be possible to estimate a standard curve that can be
used
for estimation of concentrations all the way down to zero. Therefore an
unacceptably high bias below a certain number, LLOQ, and only a small
or no
bias above LLOQ, means that a proper standard curve has not been
estimated.
But bias or not, personally I would still prefer to get the numbers
observed
instead of just the information that they are small. One thing is
certain,
to leave values below LLOQ out and consider them as missing will
introduce
bias in the estimates of parameters like halflife and clearance.
But isn't it possible completely to avoid observations below LLOQ in the
assay? Sometimes, if a value is too high, i.e. above an ULOQ, the
sample is
diluted in order to get a value in the range where the analysis method
is
validated. Why not do the same, i.e. the opposite, when an observed
value
is below LLOQ? I am certainly not an expert in this field, but it seems
so
obvious to me, that I wonder whether it not done somewhere. However, I
have
not heard about it.
For instance, we have a sample of 1 ml with a concentration x of some
compound, and the observed concentration is below LLOQ. Then it can be
mixed
with 1 ml containing a concentration of 2LLOQ of the same compound
resulting
in 2 ml with a concentration y = (x/2)+LLOQ. As y is at or above LLOQ,
the
analysis method is validated for analysis of this mixed sample, and
x = 2(y-LLOQ) is therefore by definition determined without significant
bias.
Kind regards
Poul Chr. Pedersen
[Interesting idea - seems to speak to having a good estimate of the
assay ("sample") error at low concentrations. If a 'number' is
generated below LLOQ could they be given a large and appropriate
variance thereby included in the PK analysis...adding 2LLOQ to a sample
would make for an interesting statistical analysis of the assay
("sample") error - db]
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The following message was posted to: PharmPK
Dear Dr. Pedersen,
I fully agree with the first part of your message about values below
LLOQ. Even in case of some bias I would prefer to include these values,
of course, with an appropriate weighting (variance including the
squared bias). If bias is relatively large, there is a problem, but in
that case the problem should be solved by the analytical department,
not by the pharmacokineticist!
Your suggestion about adding a known amount to values below LLOQ is
interesting, but needs of course to be supported by some practical
evidence that the obtained result is sufficiently reliable, i.e. that
it fulfills the requirements of accuracy and precision similar to that
for value above LLOQ.
I have some doubts that this will work. Addition of a known amount
always introduces errors due to pipetting etcetera. This error affects
the estimated amount in the sample. After subtraction of the known
amount the error is still in the smaller value, and may become
relatively large. Moreover, the reason for the existence of a LLOQ
should be considered. e.g. if this is simply due to noise in the
detector, your method will probably not work. In conclusion, although
interesting, I am afraid that this suggestion is a attempt to help
yourself out of the morass.
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.farm.rug.nl
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Dear Poul Chr. Pedersen,
The concept of using 10*sigma as the LOQ has long been a tarnished
idea, but it persists because it is so easy to calculate.
An alternative approach of using a Repeatability criteria instead is
discussed and recommended in the FDA's Reviewer Guidance Validation of
Chromatographic Methods, November 1994, p.10.
Frank
Frank Bales, Ph.D.
Senior Regulatory Consultant
Worldwide Regulatory Affairs
PAREXEL Intl.
2520 Meridian Pkwy, Suite 200
Durham, NC 27713
(613) 657-3010 Current Phone
(919) 294-5297 Phone at Office
Email: frank.bales.-a-.parexel.com
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The following message was posted to: PharmPK
Dear all,
To continue the discussion on handling of values below LOQ I would like
to
ask your opinion on the handling of the specific early data points
collected
after oral administration; i.e. data points before Cmax.
How do you handle these when below LOQ, if you cannot include them in
your
PK calculations (I belive this is not an option in *regulated*
toxicokinetic
studies)?
Intuitively I agree with what most people on this list seem to think -
that
a serum concentration is not zero just because it's below LOQ. But with
the
only alternative I see (again assuming you cannot just use theresult)
of excluding the data point(s) altogether, you will overestimate the
AUC. Of
course, with the first apporach you may underestimate the AUC, so i
suppose
the question should be: what apporach is the least erroneous?
Best regards,
Claus Larsen, M.Sc.(pharm)
Department of Early Development Pharmacokinetics
Non-Clinical Safety Research
H. Lundbeck A/S
Ottiliavej 9, DK-2500 Valby
Ph: +45 3644 2425 ext. 2844
Fax: +45 3630 1509
cll.-a-.lundbeck.com
[My concern with early oral data points (above the LOQ) is how
accurately do you know the sample time! - db]
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Hi Poul Christian,
I will try to add my two cents to the discussion.
First there is a human/social aspect of it. You have to build good
relations with the analytical laboratory personnel.
Each one, pharmacokineticists or chemists, should understand the needs
and the difficulties of each others work.
In my experience this helps in obtaining values not quite validated,
extending the concentration range (up or down) and repeating the assay
of some suspected samples.
The scientific side of the issue is as follows:
1) The mathematical model used to convert instrument response in
analyte concentration may not hold true outside the validated range:
LOQ to ULQ (upper limit of quantitation. There is no evidence/proof
that below LOQ the same mathematical model links the instrument
response to the analyte concentration in the sample. It is not
difficult to imagine a linear relationship within the validated range
and a quadratic or exponential model outside, at either end.
2) If the LOQ is a limitation due to the ratio between signal
and noise the chemist can try to work around the problem. The issue
becomes now a business question. How much money your management is
ready to spent for those few BLOQ values? Meaning how much man-hour are
going to be allocated to solve this issue? You must make your case!
3) The validated concentration range can be extended relatively
easily and cheaper by relaxing the validation requirements. For the low
concentration values you may be happy to agree to a +/- 30% acceptable
error instead of the commonly used +/- 20% or +/- 15% error.
3) Your suggestion of adding a known amount to the BLOQ samples
in order to bring them within the validated range is an interesting one
and I would like to spent some more time on it. However, it should be
said from the outset that the BLOQ levels can end-up being within the
error that defines the measured added amount.
I would like to suggest to you in talking to the chemist to
suggest increasing the volume of raw sample to be extracted or to
increase the volume of the extracted sample that will be injected in
the chromatograph. This may work out well for some of the BLOQ samples.
4) Finally, you are absolutely right that the cut-off values of
BLOQ and ULQ is introduce a bias in the raw data set used for
pharmacokinetic analysis.
Hope this help,
radu
Radu D. Pop
Director Biopharmaceutics
Pharma Medica Research Inc.
966 Pantera Drive
Mississauga, Ontario
Canada, L4W 2S1
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The following message was posted to: PharmPK
Claus,
There are ways to formally include censored data into the estimation of
PK
parameters. Look at the following paper in Environmental Health
Perspectives. While the analysis is not directly aimed at PK data, the
likelihood is general to any data of this type. We have several PBPk
models
in press using the same strategy. If you have questions, I will be
happy to
answer them.
Koo, J.W., Parham, F., Kohn, M.C., Masten, S.A., Brock, J.W., Needham,
L.L.,
Portier, C.J. The association between biomarker-based exposure
estimates for
phthalates and demographic factors in a human reference population.
Environ
Health Perspect 110(4): 405-10
C.
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Dear All:
About LOQ. What is the problem? It is true, in toxicology, we
have no other information except what is in the sample itself. In that
situation we must ask if the drug is present or not, and there clearly
is a LOQ. But in PK work, we know pretty well when the doses were given
and when the samples were drawn. We also know that the elimination of
most drugs is exponential. Therefore, in PK work, the drug is always
STILL THERE - the only question is HOW MUCH, not "is it there or not -
a totally different toxicological question. Please see Therap Drug
Monit 15: 380-393, 1993. I do not understand why this controversy goes
on and on and on, seemingly forever. It is very easy to resolve and
deal with. Please look at the article and tell me what you think.
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.at.usc.edu
Our web site= http://www.lapk.org
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Hi Poul: This is an interesting subject.
Briefly, your suggestion to add a known amount of standard to your
sample will not give you a more reliable result.
1) The LOQ is the lowest concentration that can be measured with the
accuracy, precision and variability required to make scientifically
sound conclusions about the drugs pharmacokinetics. For studies that
are acceptable to regulatory agencies, the LOQ is defined as the lowest
concentration that you can measure with not greater than 20% RSD intra
and inter day precision. Delta 10 isn't really used anymore. Note that
20% is twice the imprecision allowed for any other concentration on the
standard curve. Regulatory guidelines in Canada (not sure about US)
specifically require the Lab to report these values as BLQ, Below Limit
of Quantitation.
2) The imprecision is a function of the signal to noise ratio of the
analytical system. There is a certain amount of noise below the signal
associated with your LOQ (or lower, or any concentration for that
matter). You cannot change this ratio by adding a known amount to your
LOQ, and then subtracting the known amount. You are still left with the
same ratio, and the same amount of imprecision.
3) Diluting a sample that is above the ULQ is not analogous to the
idea of adding a known amount to a BLQ sample. However, Radu is
correct, it is analogous to using a larger aliquot of serum (or other
matrix). If you are above the ULQ, you can extract from half the
aliquot of serum, if you are below the LLOQ, you can extract from twice
as much serum (usually there is not enough).
4) Actually, the method recommended by Shah, et al to improve method
precision is to increase the number of replicate analysis, rather than
the sample volume. However, the number of replicates is usually
limited by the amount of sample available too. Sometimes this can be
overcome by taking two samples during times when concentrations are
expected to be low.
5) When your lab reports BLQ or LLOQ, usually there isn't much the lab
can do to with those samples. Usually, it's back to the drawing board
for the method, or the study design. However frustrating it is to know
that there is drug present, we have to ask ourselves how unreliable a
result will we accept as valid. I have seen data where the last few
concentrations on the curve (below the LOQ) appear to be increasing!!
What would you do with that? What does that say about the next curve
where the last few concs. below LOQ are decreasing, as expected?
Hopes this helps.
Peter Gingras
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The following message was posted to: PharmPK
Peter,
A value below LOD is not without information. It certainly is less
than a
known value, but still contributes to the overall information from the
data.
If the sample contains less than 30% below LOD, usually the method I
described earlier (Environmental Health Perspectives article by Koo et
al)
helps considerably in the estimation of PK parameters without
introducing
bias in the estimates.
C.
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[Two replies - db]
From: James Hillis
Date: Wed Feb 19, 2003 9:34:10 AM US/Central
To: david.at.boomer.org
Subject: RE: PharmPK Re: Values below LLOQ
Reply-To: James Hillis
The following message was posted to: PharmPK
Hi,
This is a very interesting topic for the analytical chemist, such as
myself.
Radu made some important comments. Firstly, it is vital that the
analysts
and the pharmacokineticists know what each require from the other. The
simple answer to the problem of how to reportreduce the
LLOQ of the analytical method to an acceptable level. This is a
continuous
requirement on the analyst. If the two parties do a 'back of the
envelope'
calculation they should be able to make some estimate of the Cmax and
the
LLOQ required.
A great deal of time and effort goes into assessing the quality,
accuracy,
precision etc. of data from GLP studies. Consequently there is little
or no
confidence in data outside the range (LLOQ-ULOQ) as no assessment of the
data has been made. This data cannot be released to the user with the
same
confidence as within range data, and they cannot be used in regulatory
submissions as they have not been analysed within the validated range
of the
method. The LLOQ and ULOQ of the analysis should be decided before the
start of the study. Then there are no nasty gaps in profiles!
Another point that Radu made, the addition of analyte to samples to
bring
them within range. I have not seen this used in bio-analysis. However,
this is a widely used technique in analytical chemistry. It is known as
standard addition. I have wondered for some time if this could be used
to
extent the limits of detection for analytes in bio-analysis? I would
like
to know what the other members of the group think about this, pros and
cons
and the regulatory stand point? I wonder if you validated a method as
such,
would it be accepted as part of a regulatory submission.
James Hillis
jhillis.-at-.hfl.co.uk
---
From: pgingras.-a-.apotex.com
Date: 19 Feb 2003
Hi Christopher: I agree, there is some useful information there. For
values below LOQ, you can certainly conclude that the drug hasn't
completely cleared, or that absorption has begun. Drug regulators do
not accept calculations based on numbers outside of your validated
range though. I believe this is the reason that they require the data
to be presented as BLQ (or LLOQ), rather than zero.
Once the values fall below your LOQ, one usually doesn't know the
imprecision of the value. One knows what the imprecision is at the LOQ
(20%), but lower values should be expected to have even greater
imprecision.
If you really want to know just how much error is associated with these
very low values, go into your lab and ask your chemist to run a drift
check on the analytical system. Have your chemist repeat the check on
a few different days. You might even want to watch while the test is
running, it only takes a few minutes.
The LOD (limit of detection) is different from the LOQ. One should
completely ignore results approaching (certainly below) the LOD.
Results below the LOD are zero, for all intents and purposes.
I think it this is an interesting discussion partly because the
measurement errors (and our understanding of them) are so important to
the quality of our science. For example, I have seen a study that
"proved" a statistically significant 2 mmHg differences in blood
pressure effect, when blood pressure was only reported in 5 mmHg
increments. Of course the difference was entirely artifactual.
Peter
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