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: [email protected] [mailto:[email protected]]
On Behalf Of Leonid Gibiansky
Sent: 12 January 2009 23:30
To: Bonate, Peter
Cc: [email protected]
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
[email protected]_ <mailto:[email protected]>
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
alea jacta est - The die is cast.
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