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Q 1. LLQ is the lower limit of quantitification. Do regulatory
Pharmacometric groups endorse?
a. Ignoring LLQ values
b. Imputing LLQ values as 0
c. Imputing LLQ values as 0.5*LLQ
d. Using the actual measurement i.e. ask the chemical analyst to tell
the truth
e. None of the above
Q 2. Beal S. Ways to fit a pharmacokinetic model with some data below
the quantification limit. Journal of Pharmacokinetics and
Pharmacodynamics 2001;28(5):481-504
Has there been any advance on this in the last 4 years?
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/
[Q1. a Ignore value below LLQ? Best of the choices?; b and c could
confuse the fitting process; d with appropriate weight may be better
than a; or e ;-)
Q2. Search http://www.boomer.org/pkin/simple.html for llq, log, or
'lower limit of quantitation' ? - db]
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The following message was posted to: PharmPK
Thanks to those who took the test and responded to me. Not all
responses were sent back to the open lists so I have anonymised all the
responses.
Question 1
========Extra marks were given to the PharmPK user who pointed out I
should have used BLQ instead of LLQ.
"I think what you meant to say in items 1(a) to (c) is "BLQ" (below the
limit of quantitation) instead of "LLQ", since a value that is at the
LLQ can just be reported as such as it is contained within the
validated range."
Quite correct! What I meant to ask would have been better expressed as
follows. I have changed "LLQ" to "LLOQ" and use "quantification" (not
"quantitation") for consistency with the FDA Bioanalytical guidance
(see below).
Q 1. LLOQ is the lower limit of quantification. Measured concentrations
less than LLOQ are said to be below the limit of quantification (BLQ).
Do regulatory Pharmacometric groups endorse?
a. Ignoring BLQ values
b. Imputing BLQ values as 0
c. Imputing BLQ values as 0.5*LLOQ
d. Using the actual measurement i.e. ask the chemical analyst to tell
the truth
e. None of the above
The most definitive material pertinent to Q1 came from the following
quote from the Code of Federal Regulations. It was provided by a ex
senior FDA person who would have dealt commonly with this kind of
issue. This person and another current senior FDA person said they knew
of no FDA guidance requiring the use of LLQ to modify data used for PK
analysis.
"Sec. 320.29 Analytical methods for an in vivo bioavailability or
bioequivalence study.
(a) The analytical method used in an in vivo bioavailability or
bioequivalence study to measure the concentration of the active drug
ingredient or therapeutic moiety, or its active metabolite(s), in body
fluids or excretory products, or the method used to measure an acute
pharmacological effect shall be demonstrated to be accurate and of
sufficient sensitivity to measure, with appropriate precision, the
actual concentration of the active drug ingredient or therapeutic
moiety, or its active metabolite(s), achieved in the body."
There is a 2001 Bioanalytical Method Validation guidance that defines
LLOQ as concentrations with 20% CV
(http://www.fda.gov/cder/guidance/4252fnl.pdf). It says nothing that I
can see about whether LLOQ should be applied when doing a PK analysis.
Note that Bioanalytical Method validation statistics such as LLOQ are
used to describe the properties of the assay. This guidance does not
define how the concentrations are to be used.
A subsequent 2003 Bioavailability and Bioequivalence document describes
PK procedures but does not mention the use of LLOQ
(http://www.fda.gov/cder/guidance/5356fnl.pdf).
There seems to be a common mis-perception that FDA requires the use of
LLOQ in a PK analysis however no-one has provided any written evidence
of this policy so far.
My interpretation of these responses is that the closest answer to Q1
should be:
"d. Using the actual measurement i.e. ask the chemical analyst to tell
the truth"
Question 2
=========Almost full marks to the nmusers peson who gave a list of
references of various opinions on dealing with BLQ values. Some credit
was lost for using an obscure (Latex) character based formatting
convention and providing a non-retrievable reference to recent work
attributed to M. Tod.
A prominent user of NONMEM responded:
"The only advances have been
I) my increasing conviction that whenever the pattern of BLQ values is
consistent with the observed PK, that (a) [ignoring BLQ values], along
with the adjustment described by Beal (2001) to account for the bias,
is the way to go, and
(II) the addition of a feature in NONMEM version VI that allows this
sort of thing to be easily done."
Nick
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The following message was posted to: PharmPK
Nick,
Your option
d. Using the actual measurement i.e. ask the chemical analyst to tell
the truth" should
help to limit LLOQ somehow but at the end you will still get some zero
values that are measurements below LLOAATDCFZ (lower limit of assay
ability to distinguish concentration from zero). Then, you will need to
choose among 3 other options:
a. Ignoring 0 values
b. Using 0 values as 0
c. Imputing 0 values as 0.5*LLOAATDCFZ
Remembering the advice of "a prominent user of NONMEM" (I am not sure
whether this is the same user as your adviser, but I found on more than
one occasion that the advices were good), I usually use (a). Do you
have any examples where this would lead to the incorrect model? Also,
have you found any examples where option (d) was better (resulted in a
more precise or more stable model) than option (a)?
Unfortunately, information concerning NONMEM VI is not relevant to the
most of mortals except those few who were granted this tool (I guess,
as a recognition of the special contribution to the NONMEM
development).
Thanks
Leonid
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Leonid,
LL0AATDCFZ and its bigger brother LLOD (lower limit of detection) are
just as arbitrary and capricious as LLOQ when it comes to PK analyis. I
accept they can be helpful statistics for those involved in the care
and feeding of bioanalytical methods.
However, if the chemical analyst (or the computer connected to the
measuring device) was required to report the truth then if the
concentration was really zero it should report a random variable with
mean 0 (assuming the measurement process does not get truncated at
zero). The variance of this random variable is a component of the
additive residual error we estimate every day for PK models. So I don't
see any need to apply LL0AATDCFZ. Just give me the true measurement
value.
One thing is sure about the true concentration -- until sufficient time
has passed for less than one molecule to be left in the body then the
concentration is not 0. This is longer than most people live...
Stuart Beal has offered some examples of what happens if answer (a) is
used (treat BLQ values as missing). You can also find some more
examples in Duval V, Karlsson MO. Impact of omission or replacement of
data below the limit of quantification on parameter estimates in a
two-compartment model. Pharm Res 2002;19(12):1835-40.
I'm afraid I don't have any personal experience comparing the true
measurement with the obscured values reported by chemical analysts.
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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The following message was posted to: PharmPK
Nick,
Thanks for the reference, results seems very reasonable: if you ignore
zeros, predicted concentrations may decay not as fast as they should
(leading to lower CL, higher V). However, this might be strongly
related to the design and sampling. In my examples, fraction of BQLs
was relatively small (less than 5%), most zeros were very suspicious
(related either to the non-compliance or data errors) because LLOQ was
3-4 orders of magnitude less than Cmax while sampling points were not
that far from the dose to warrant zeros. With the good design, fraction
of BQLs in the data set is small, and efforts that are needed to
include those are not warranted by the gain that you may get from
inclusion of those points.
As to the true values, you may be forced to use special segment of the
error model to account for the BQL measurements. This can be very
similar to LLOQ/2 imputation with BQL variance fixed at (LLOQ/2)^2.
My justification of the idea to ignore zeros (or not to use "true"
values) is that we are not interested in the very fine details of the
PK behavior (the deeper you look, the more compartments you may
discover) and restrict the model to the range of concentrations that
are relevant to your problem. Sampling should also be consistent with
the goal of the study: samples should be located at characteristic
points of the profiles (while BQLs are definitely not in that
range/position).
One can imagine situations when zeros are important: for example, if
there is a sub-population with much higher CL: ignoring zeros may hide
the fact that concentration decay for a sub-population is much faster
than was expected, especially if the sample timing was not designed for
the sup-population with the high CL. But even in this case, BQL values
may help you to discover the problem with your design, but will not
help to build the correct model: it is difficult to build correct model
based on the very noisy measurement. If you do not have sufficient
non-BQL time points to define the terminal phase and impute some BQL
values (or use the true value that will be a reflection of the random
noise generated by the instrument), the model for the subpopulation
will be defined by the timing of the sampling point rather than by the
actual CL. If you have sufficient number of non-BQL time points to
define the terminal phase, ignoring the BQLs should not adversely
affect the model.
Leonid
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Leonid,
Your discussion agrees with what Stuart Beal wrote. In most cases
treating BLQ values as missing is fine. In some special cases there is
a small amount of useful info from knowing that it is BLQ (but not
missing). Imputation of BLQ with LLOQ/2 is a quick and dirty way to
partially recover some of this information.
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
Nick:
Thank you for two things: 1) keeping once a year
ritual of BQL data treatment discussion alive, 2)
acknowledging usefulness of Imputation of BLQ with
LLOQ/2 in some cases. Everyone including you mentioned
it takes too long for the last molecule to leave the
body and this is probably true for the residual amount
of drug in the body but to a lesser extent. Then
setting BQL values at zero goes against what we just
said, ignoring BQL data = exclusion of valuable
information, so two other approaches comes to mind: 1)
treating the data using models/statistics/fancy
weighting methods etc (e.g., Roger's approach - Hello
Roger, I hope continuing discussion on this subject
does not bother you) and 2) using LLOQ/2 which is
easy, fast (you call it a quick and dirty way, I call
it practical and reasonably adequate) and as you said
partially recover some information (not as bad is
giving zero or discarding info and perhaps not as
scientifically sound as first approach).
Rostam
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)