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From: "Cory Langston"
Date: Fri, 30 May 2003 08:42:24 -0500
Subject: Superpositioning: How far to predict missing points
The following message was posted to: PharmPK
I'm part of a project called the Veterinary Antimicrobial Decision Support
(VADS) system. A large part of what we're doing is reviewing the kinetic
information on various antimicrobials in food animals, comparing
susceptibility profiles of common bacterial pathogens, and proposing
suggested dosage regimens for review. (It's really more complicated than
that, but the above is a 'bottom line' synopsis.). Anyway, we've found
that there are very few complete kinetic models to draw on but we can
however usually get at the mean time-concentration profile and associated
SDs. Accordingly, we're using superpositioning (SP) quite a bit.
I'd like to ask for opinions on an issue that we're dealing with in VADS
relative to SP. Of course unlike in the textbook examples of SP where the
samples are all taken at equal intervals, real sampling protocols tend to
have frequent samplings early on and then fewer toward the terminal phase.
When overlaying the dosings this leaves gaps that must be dealt with in
order to produce a profile that accounts for carryover from prior dosings.
An example is from the following dataset of procaine penicillin G showing
superpositioning of the first two doses.
Hour Dose 1 Dose 2
0 0 ~
0.5 0.87 ~
1 0.68 ~
2 0.61 ~
3 missing ~
4 0.38 ~
5 missing ~
6 missing ~
7 missing ~
8 0.15 ~
9 missing ~
10 missing ~
11 missing ~
12 missing 0
12.5 missing 0.87
13 missing 0.68
14 missing 0.61
15 missing missing
16 missing 0.38
17 missing missing
18 missing missing
19 missing missing
20 missing 0.15
21 missing missing
22 missing missing
23 missing missing
24 missing missing
For missing data in the non-terminal phase, we've been regressing the two
points on both sides and then using that regression equation to predict
the missing point. For the terminal phase, we've been regressing the last
points that appear associated with the terminal phase, typically the last
3 to 5 points, and then using that equation to predict the missing
intermediate points and where necessary, the missing points beyond the
last sampling. It is the latter approach that I'm seeking an opinion on.
Specifically, how far should we predict missing data points beyond the
last sampled point?
In this regard we have proposed several possibilities including:
a) Predicting for at least 2x the dosing interval. For example, making
sure that if a q12h interval is being predicted then we would want the
single-dose data extrapolated to 24 hours. This assures that for each
succeeding dose interval any residual drug from the prior dose is added to
it. The disadvantage is that for low doses we are adding inconsequential
concentrations and, when we predict high doses using dose proportionality,
substantial concentrations greater than 2x the dosing interval might not
be accounted for.
b) Predict to and then cut-off at 1/3 of the lowest tested MIC dilution.
For example, if the MIC dilution panel for penicillin G goes down to 0.125
mcg/ml, we would make sure than concentrations are predicted to 0.33 x
0.125 = 0.04125 mcg/ml. Concentrations falling below this would be
ignored as inconsequential. (This proportion was selected based on our
review of the literature which showed some standard deviations at the
terminal phase to be as high as 200%. As we are using Monte Carlo
simulations to predict population concentrations, the variance or standard
deviations are used to build the distributions; therefore, a standard
deviation that is 200% of the mean could potentially add a meaningful
amount to the concentration. If the lowest concentration extrapolated is
less than 1/3 the lowest dilution, then even coefficient of variation of
200% would still NOT bring many of the simulated concentrations to that
dilution, meaning it is inconsequential in terms of changing the final
concentration.) This at least sets some definition of what constitutes a
consequential carryover concentration. When we
proportionality we however run into the situation where we will be
predicting concentrations for a shorter time frame when lower doses are
modeled than when higher doses are modeled.
c) Predicting the more 'conservative' of a or b, where 'conservative'
means that less accumulation and hence lower plasma concentrations are
produced. In so doing, we err on the side of producing higher doses and
hence a greater probability of therapeutic success (albeit a greater
chance of residues).
d) Predicting the more 'liberal' view of a or b, where 'liberal' means
that the method producing more accumulation would occur. This may better
account for true carry-over from prior doses. The thought being if that
carryover is large, then we should account for it. If the carryover is
small, then it really doesn't matter.
Of course the bottom line to all of this is that there probably really
isn't a single correct answer. It really depends on what one defines as
'significant' carryover from a dose. Still, we need to establish some
form of working SOP and would appreciate your views.
Thanks in advance,
Cory Langston, DVM, PhD, DACVCP
College of Veterinary Medicine
Box 6100 (Spring Street for courier)
Miss. State, MS 39762-6100
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