From: Leonid Gibiansky <*LGibiansky*>

Date: Tue, 13 Jan 2009 15:37:13 -0500

Nick,

Just to set the record straight:

I did NOT proposed model (1):

TVCL=THETA(1)*(WT/70)^(3/4) + THETA(2)*(WT/70)^(3/4)

Rather I mentioned that this is not an appropriate model.

Model 2 is indeed empirical. Instead of BSA you can use WT^(3/4) or any

other normalization:

TVCL=THETA(1)*(WT/70)^(3/4) * RF^GAMMA

RF is the renal function.

GAMMA is the fudge factor. You can set it to one or replace RF^GAMMA by

other empirical function of RF, e.g., 1+THETA()*RF. The point is that

renal impairment may influence not only renal clearance itself but also

a lot of other body functions (metabolism, in particular). Linear

dependence (that you mentioned) may or may not be sufficient to account

for these changes.

Use of categorical covariates, indeed, sacrifices some information but

it can be used to detect whether it makes sense to use more

detailed/mechanistic models: if categorical description does not show

any renal impairment effect, it makes no sense to use more complicated

models, and it makes sense to explain dependence of CL on CRCL by WT,

AGE or other available covariates.

Best

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Nick Holford wrote:

*> 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-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 - 15:37:13 EST

Date: Tue, 13 Jan 2009 15:37:13 -0500

Nick,

Just to set the record straight:

I did NOT proposed model (1):

TVCL=THETA(1)*(WT/70)^(3/4) + THETA(2)*(WT/70)^(3/4)

Rather I mentioned that this is not an appropriate model.

Model 2 is indeed empirical. Instead of BSA you can use WT^(3/4) or any

other normalization:

TVCL=THETA(1)*(WT/70)^(3/4) * RF^GAMMA

RF is the renal function.

GAMMA is the fudge factor. You can set it to one or replace RF^GAMMA by

other empirical function of RF, e.g., 1+THETA()*RF. The point is that

renal impairment may influence not only renal clearance itself but also

a lot of other body functions (metabolism, in particular). Linear

dependence (that you mentioned) may or may not be sufficient to account

for these changes.

Use of categorical covariates, indeed, sacrifices some information but

it can be used to detect whether it makes sense to use more

detailed/mechanistic models: if categorical description does not show

any renal impairment effect, it makes no sense to use more complicated

models, and it makes sense to explain dependence of CL on CRCL by WT,

AGE or other available covariates.

Best

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Nick Holford wrote:

Received on Tue Jan 13 2009 - 15:37:13 EST