# Re: CrcL or Cr in pediatric model

From: Leonid Gibiansky <LGibiansky>
Date: Tue, 13 Jan 2009 10:41:30 -0500

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.

> 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-nmusers
> On Behalf Of Leonid Gibiansky
> Sent: 12 January 2009 23:30
> To: Bonate, Peter
> Cc: nmusers
> 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.bonate
>> phone: 210-949-8662
>> fax: 210-949-8219
>> crackberry: 210-315-2713
>>
>> alea jacta est - The die is cast.
>>
>> Julius Caesar
>>
>>
>
Received on Tue Jan 13 2009 - 10:41:30 EST

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