Leonid,
You propose two models
Model 1: TVCL=THETA(1)*(WT/70)^(3/4) + THETA(2)*(WT/70)^(3/4)
Model 2: TVCL=THETA(1)*(WT/70)^(3/4) * (CRCL/BSA)^GAMMA
As you say, Model 1 clearly is not identifiable to distinguish THETA(1)
and THETA(2). An identifiable model would be:
Model 3: TVCL=(THETA(1) + RF*THETA(2)) * (WT/70)^(3/4)
Here RF is the renal function. Note I use renal function as a relative
measure of the function of the kidney which is the way it is typically
used in clinical practice e.g. one says 'this patient has normal renal
function' or 'this patient has poor renal function'. In previous
publications (eg. see Mould 2002, Matthews 2004, Anderson 2007) I have
used the RF factor to identify the relationship between a biomarker such
as CLcr and the renal component of clearance. Note that RF is size
independent. Size is applied, independently, to both the non-renal
(THETA(1)) and the renal clearance (THETA(2)) through theory based
allometric scaling.
Model 3 is mechanism based and can be used to test mechanistic
hypotheses e.g. is renal clearance linearly related to RF? and extended
e.g. is there a drug interaction on non-renal clearance with a known
metabolism inhibitor which is not expected tochange renal elimination?
Model 2 is quite empirical. It uses BSA for scaling althought this is
known to have a poor theoretical foundation and is worse than theory
based allometry using WT^3/4 when these models are tested using GFR in
relation to size (Rhodin 2008). The gamma parameter has no physical
intepretation. The model cannot distinguish the effect of a metabolic
inhibitor on non-renal clearance. I cannot see any point in using this
model unless you are just a statistician interested in generating P values.
The interesting challenge is how to define RF. In adults (Mould 2002,
Matthews 2004) this has been done relative to a 'normal' standard
CLcrSTD of 6 L/h/70kg. Individual CLcr was predicted using Cockcroft &
Gault (Mould 2002) or with a very similar but mechanistically enhanced
model in Matthews (2004). The individual CLcr prediction was based on
age, sex and serum creatinine but the prediction was standardised to 70
kg. The RF was then calculated from CLcr/CLcrSTD.
In children it is possible to predict Clcr using height and the Schwartz
formulae which were empirically derived for different age groups and
unfortunately scaled to a BSA of 1.73M^2. Very frequently one has only
got weight so it makes the Schwartz method more difficult to use. It is
possible to predict BSA from weight alone in children (1935) then use
the DuBois & DuBois formula with weight to determine an appropriate
height. In this way one can use just weight alone to predict CLcr
(uncorrupted by BSA) in different age groups of children. Other methods
have been proposed e.g. Leger (2002), Cole (2004) but these have been
developed in older children and the Cole method can predict negative
values (see Anderson 2008).
The method for predicting RF in children is to use the GFR prediction
model (Rhodin 2008) to obtain a 'normal' GFR based on maturation and
size. Then predict individual CLcr using a model to predict creatinine
production rate (CPR) and dividing by the measured serum creatinine
(Scr). ie. CLcr=CPR/Scr. The RF is then calculated similarly to adults
from CLcr/GFR. In adults CLcr is quite close to GFR but in young
children the CLcr is typically higher than GFR by 15% or more
(Hellerstein 1992). Because there are no good standards for Clcr in
children and because GFR is a biomarker more closely related to the
function of the kidney overall the 'normal' GFR is preferable to a
'normal' CLcr.
I am currently working on an extension to the model proposed in Anderson
(2007) which uses vancomycin clearance and GFR observations to deduce
how CLcr can be predicted from maturation and size from very premature
neonates to young adults. This new CLcr method has shown itself capable
of identifying RF variation in neonates which substantially reduces
between subject variability in neonatal vancomycin clearance (18%
compared with 28%) (work in progress).
Leonid asked these questions in an earlier response to Peter. I have
added some comments:
1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get
rid of WT - CRCL dependence. If you need to use it in pediatric
population, normalization could be different but the idea to normalize
CRCL by something that is "normal CRCL for a given WT" should be valid.
BSA is a bad idea. It is provably worse than WT^3/4 (Rhodin 2008) and is
persists through tradition and a mistaken allometric theory developed
over 100 years ago (See Anderson 2008).
Normalization to "normal CRCL for a given WT" is a good idea and in a
more complex form is what I have described above (WT alone is not good
enough for neonates -- post-menstrual age must be included too).
2. In the pediatric population used for the analysis, are there any
reasons to suspect that kids have impaired renal function ? If not, I
would hesitate to use CRCL as a covariate.
In general I agree with you that in most cases there is no need to
suspect renal function impairment in children. Indeed the big problem
has been how to know if renal function impairment existed. Impairment
implies that the non-impaired normal value is known. The work of Rhodin
(2008) finally provides a method predicting normal GFR but it was a
necessary assumption of that analysis that all the GFR measurements were
made in children without renal disease.
3. Often, categorical description of renal impairment allows to
decrease or remove the WT-CRCL correlation
Categorical descriptions are necessarily less informative. You just
throw away information by putting people into boxes. It is a way of
hiding the problem not solving it.
So in conclusion I encourage people working in this area to use
mechanism based models to understand how renal function influences
pharmacokinetics and at the very least compare the predictions of an
empirical model (e.g. Model 2) with a mechanism based model (e.g. Model
3) so that you can understand what you are missing.
Nick
Anderson, B. J., K. Allegaert, et al. (2007). "Vancomycin
pharmacokinetics in preterm neonates and the prediction of adult
clearance." Br J Clin Pharmacol 63(1): 75-84.
Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of
size and maturity in pharmacokinetics." Annu Rev Pharmacol Toxicol 48:
303-32.
Boyd, E. (1935). The growth of the surface area of the human body.
Minneapolis, University of Minnesota Press.
Cole, M., L. Price, et al. (2004). "Estimation of glomerular filtration
rate in paediatric cancer patients using 51CR-EDTA population
pharmacokinetics." Br J Cancer 90(1): 60-4.
DuBois, D. and E. F. DuBois (1916). "A formula to estimate the
approximate surface area if height and weight be known." Archives of
Internal Medicine 17: 863-871.
Hellerstein, S., U. Alon, et al. (1992). "Creatinine for estimation of
glomerular filtration rate." Pediatric Nephrology 6: 507-511.
Leger, F., F. Bouissou, et al. (2002). "Estimation of glomerular
filtration rate in children." Pediatr Nephrol 17(11): 903-7.
Matthews, I., C. Kirkpatrick, et al. (2004). "Quantitative justification
for target concentration intervention - Parameter variability and
predictive performance using population pharmacokinetic models for
aminoglycosides."
Mould, D. R., N. H. Holford, et al. (2002). "Population pharmacokinetic
and adverse event analysis of topotecan in patients with solid tumors."
Clinical Pharmacology & Therapeutics. 71(5): 334-48.
British Journal of Clinical Pharmacology 58(1): 8-19.
Rhodin, M. M., B. J. Anderson, et al. (2008). "Human renal function
maturation: a quantitative description using weight and postmenstrual
age." Pediatr Nephrol. Epub. (please contact me if you want a pdf copy)
Leonid Gibiansky wrote:
Jakob,
Restrictions on the parameter values is not the only (and not the
major) problem with additive parametrization. In this specific case,
CRCL (as clearance) increases proportionally to WT^(3/4) (or similar
power, if you accept that allometric scaling has biological meaning or
that the filtration rate is proportional to the kidney size). Then you
have
TVCL=THETA(1)*WT^(3/4)+THETA(2)*WT^(3/4)
(where the second term approximates CRCL dependence on WT).
Clearly, the model is unstable.
Answering the question:
> why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates,
> except WT), be expected to differ by 36% in CL?
we are back to the problem of correlation. If two persons of different
WT have the same CRCL, they should differ by the "health" of their
renal function. I would rater have the model
CL=THETA(1)*(WT/70)^(3/4)*(CRCL/BSA)^GAMMA
Then, if two subjects (50 and 70 kg) have the same CRCL, their CL will
be influenced by WT, and by renal function (in this particular
realization, CRCL per body surface area). While the result could be
the same as in
CL ~ CRCL,
we described two separate and important dependencies:
CL ~ WT; and CL ~ renal function
For the patient that you mentioned, they act in the opposite
directions and cancel each other, but it is important to describe both
dependencies.
> Regarding 3 below, is the suggestion to estimate
> independent allometric
> models on CL for each level of renal function?
The suggestion was to define the renal disease as categorical
variable, and then correct CL, for example:
TCL ~ THETA(1) (for healthy)
TCL ~ THETA(2) (for patients with severe renal impairment)
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Ribbing, Jakob wrote:
Leonid,
I usually prefer multiplicative parameterisation as well, since it is
easier to set boundaries (which is not necessary for power models, but
for multiplicative-linear models). However, boundaries on the additive
covariate models can still be set indirectly, using EXIT statements (not
as neat as boundaries directly on the THETAS, I admit).
In this case it may possibly be more mechanistic using the additive
parameterisation: For example if the non-renal CL is mainly liver, the
two blood flows run in parallel and the two elimination processes are
independent (except there may be a correlation between liver function
and renal function related to something other than size). A
multiplicative parameterisation contains an assumed interaction which is
fixed and in this case may not be appropriate. If the drug is mainly
eliminated via filtration, why would two persons, with WT 50 and 70 kg
but otherwise identical (including CRCL and any other covariates, except
WT), be expected to differ by 36% in CL? This is what you get using a
multiplicative parameterisation. The fixed interaction may also drive
the selection of the functional form (e.g. a power model vs a linear
model for CRCL on CL). I do not know anything about Peter's specific
example so this is just theoretical.
Regarding 3 below, is the suggestion to estimate independent allometric
models on CL for each level of renal function?
Thanks
Jakob
-----Original Message-----
From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com]
On Behalf Of Leonid Gibiansky
Sent: 12 January 2009 23:30
To: Bonate, Peter
Cc: nmusers@globomaxnm.com
Subject: Re: [NMusers] CrcL or Cr in pediatric model
Hi Peter,
If allometric exponent is fixed, collinearity is not an issue from
the mathematical point of view (convergence, CI on parameter
estimates, etc.). However, in this case CRCL can end up being
significant due to additional WT dependence (that could differ from
allometric) rather than
due to renal function influence (that is not good if you need to
interpret it as the renal impairment influence on PK).
Few points to consider:
1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to
get rid of WT - CRCL dependence. If you need to use it in pediatric
population, normalization could be different but the idea to
normalize CRCL by something that is "normal CRCL for a given WT"
should be valid.
2. In the pediatric population used for the analysis, are there
any reasons to suspect that kids have impaired renal function ? If
not, I would hesitate to use CRCL as a covariate.
3. Often, categorical description of renal impairment allows to
decrease or remove the WT-CRCL correlation
4. Expressions to compute CRCL in pediatric population (note that
most of those are normalized by BSA, as suggested in (1)) can be found
here:
http://www.globalrph.com/specialpop.htm
http://www.thedrugmonitor.com/clcreqs.html
5. Couple of recent papers:
http://www.clinchem.org/cgi/content/full/49/6/1011
http://www.ajhp.org/cgi/content/abstract/37/11/1514
Thanks
Leonid
P.S. I do not think that this is a good idea to use additive dependence:
TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Bonate, Peter wrote:
I have an interesting question I'd like to get the group's
collective opinion on. I am fitting a pediatric and adult pk
dataset. I have fixed weight a priori to its allometric exponents
in the model. When
I
test serum creatinine and estimated creatinine clearance equation as
covariates in the model (power function), both are statistically
significant. CrCL appears to be a better predictor than serum Cr (LRT
=
22.7 vs 16.7). I have an issue with using CrCL as a predictor in
the model since it's estimate is based on weight and weight is
already in the model. Also, there might be collinearity issues with
CrCL and weight in the same model, even though they are both
significant. Does
anyone have a good argument for using CrCL in the model instead of
serum Cr?
Thanks
Pete bonate
Peter L. Bonate, PhD, FCP
Genzyme Corporation
Senior Director
Clinical Pharmacology and Pharmacokinetics
4545 Horizon Hill Blvd
San Antonio, TX 78229 USA
_peter.bon...@genzyme.com_ <mailto:peter.bon...@genzyme.com>
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
alea jacta est - The die is cast.
Julius Caesar
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holf...@auckland.ac.nz tel:+64(9)923-6730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
