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RE: Allometric scaling of renal clearance with estimated glomerular filtration rate

Date: Thu, 7 Dec 2017 13:00:51 +0000

Dear Rob,

Why do you want to use a model to predict the value of a covariate to add i=
nto your model? Apart from glomerular filtration rate, what other situatio=
ns would you do this?
Unless I was trying to do some fancy separation of renal and non-renal clea=
rance, I would simply ignore the fact there is a model to predict glomerula=
r fltration, and include its component parts e.g.

CL = THETA * (WT/70)**0.75 * FCREAT * FAGE

where FCREAT and FAGE are covariate functions for creatinine (e.g. (SECR/me=
dian value)**THETA ) and age.

Some examples of not using a model to predict GFR still gave an acceptable =
model of CL (what we were interested in):

Creatinie e.g.
Hennig S. Population pharmacokinetics of tobramycin in patients with and wi=
thout cystic fibrosis. Clin Pharmacokinet. 2013 Apr;52(4):289-301

Cystatin C example:
De Cock PA. Augmented renal clearance implies a need for increased amoxici=
llin-clavulanic acid dosing in critically ill children. Antimicrob Agents C=
hemother. 2015 Nov;59(11):7027-35.



Joseph F Standing
MRC Fellow, UCL Institute of Child Health
Antimicrobial Pharmacist, Great Ormond Street Hospital
Honorary Senior Lecturer, St George's University of London
Tel: +44(0)207 905 2370
Mobile: +44(0)7970 572435
From: owner-nmusers
 of R.terHeine
Sent: 07 December 2017 11:56
To: nmusers
Cc: n.holford
com; j.h.proost
Subject: RE: [NMusers] Allometric scaling of renal clearance with estimated=
 glomerular filtration rate

Dear Nick, Hans, Ruben, Max,

Great to hear several approaches and opinions on the use of glomerular filt=
ration approximations in PK modeling and scaling to body size. Thank you!

I have a hard time ignoring the CKD-EPI equations (with or without cystatin=
 C), as they are well established and proven better predictors for GFR, whe=
n compared to the Cockroft-Gault. In general, sample sizes of pharmacokinet=
ic studies are smaller than those where the CKD-EPI and MDRD equations were=
 developed. I am not convinced that developing a new creatinine/cystatin c =
equation for GFR for each PK analysis is the right approach. Then again, I =
also have a hard time scaling to BSA, as in, for example, obese patients th=
is is likely a poor body size descriptor to scale renal function.

Also, depending on the population and drug one may choose one equation abov=
e another. For example: if a drug is completely filtrated (no active secret=
ion), a cystatin C based equation is likely better explain variability in c=
learance of completely filtrated drugs (e.g. carboplatin). Another example:=
 in cachectic patients one may argue that there is not enough muscle mass (=
and thus serum creatinine) to provide accurate GFR estimations and then cre=
atinine-independent equations may provide better equations.

Thinking about this the last couple of days and with your feedback, I am in=
clined to choose the equation based on population (e.g. cachectic or not?) =
and drug (e.g. filtration/active secretion) and, if the equation scales ren=
al function to BSA, convert it to scaling to FFM. Nonetheless, open to any =
other suggestion or discuss cons and pro's anytime!


-----Oorspronkelijk bericht-----
Van: owner-nmusers
ens Nick Holford
Verzonden: woensdag 6 december 2017 20:06
Aan: nmusers
Onderwerp: Re: [FORGED] [NMusers] Allometric scaling of renal clearance wit=
h estimated glomerular filtration rate

Hi Rob,

Thanks for bringing this up again. I don't think much has changed since I w=
rote this in 2013

1. Theory Based Allometry or Surface Area

"Note that using surface area as a form of size standardization forglomerul=
ar filtration rate has no theoretical nor experimental support when compare=
d to theory based allometry (Rhodin et al. 2009). So I donot agree with sta=
ndardizing CLCR to 1.73 m^2. I know this is frequently done but in fact thi=
s is just based on tradition and an out of datetheory of scaling based on s=
urface area (see Anderson & Holford 2008)."

There is no biological or experimental support for using surface area to sc=
ale renal function markers such as GFR and CLcr. In contrast, there is str=
ong biological based theory and experimental support for using theory based=
 allometry (see Holford & Anderson 2017 for a recent review).

2. Mechanism Based Models for CLcr

I also wrote in 2013:

"The MDRD method of predicting glomerular filtration rate is astatistical a=
bsurdity which does not include any measurement of size for its prediction.=
 I would certainly not recommend using it for anyscientific purpose. "

This applies equally well to the CKD-EPI method. Let me explain why it is a=
 absurdity generated by a naive statistician using CLcr as an example.

CLcr can be calculated from the creatinine excretion rate (CER) and the ser=
um creatiniine. This is based on the definition of clearance and is true wi=
thout any assumptions.
If we then assume Scr is at steady state then CER will be equal to creatini=
ne production rate (CPR) and we can use this:
All rational models for predicting CLcr without measurement of CER use mode=
ls to predict CPR e.g.

CPR=(140-Age)*Weight/72 use Cockcroft & Gault to predict CPR in males th=
en CLcr=CPR/Scr is Cockcroft & Gault CLcr ml/min

Dividing CPR by Scr gives the CLcr. This can be written equivalently but le=
ss clearly:

The empirical models such as MDRD and CKI-EPI (see below) involve the absur=
dity of estimating the known exponent for Scr of -1. These estimates must b=
e wrong based on the theory I have outlined above (unless the estimate is e=
xactly -1). The reported estimates are -1.209 for CKI-EPI and -1.154 for MD=

In addition, and more importantly,they have no direct measure of body size =
which seriously limits the value outside the typical weight distribution an=
d they are only applicable to adults. GFR can be described from premature n=
eonates to adults using theory based allometry and maturation based on post=
-menstrual age so GFR predicttions should try to follow the concepts used t=
here (Rhodin 2008).

So what to do?

First -- don't use MDRD or CKI-EPI unless you are sure you are applying the=
m to a population similar to that used to develop these empirical predictio=
ns. You could add allometric scaling to the eGFR by assuming the 1.72m^2 va=
lue is equivalent to 70 kg with a fat free mass (FFM) of
56.1 kg. Then scaling the eGFR by (WT/70)^(3/4) or (FFM/56.1)^(3/4).

I use the Schwartz (1992) equations for neonates, children and teenagers th=
en the Matthews (2004) equation for adults. I am working on an integrated m=
ethod for CPR prediction which was presented as a work in progress at PAGE =
this year. Watch this space...

Best wishes,


        eGFR =175 x (SCr)^-1.154 x (age)-0.203 x 0.742 [if female] x
1.212 [if Black]

       eGFR = 141 x min(SCr/k, 1)^alpha x max(SCr /kappa, 1)^-1.209 x 0.9=
93^Age x 1.018 [if female] x 1.159 [if Black]
       kappa = 0.7 (females) or 0.9 (males)
       alpha = -0.329 (females) or -0.411 (males)

eGFR (estimated glomerular filtration rate) = mL/min/1.73 m2; SCr (standa=
rdized serum creatinine) = mg/dL

Holford NHG, Anderson BJ. Allometric size: The scientific theory and
extension to normal fat mass. Eur J Pharm Sci. 2017;109(Supplement):S59-S64=

Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
Chatelut E, Grubb A, Veal GJ, Keir MJ, Holford NH
Human renal function maturation a quantitative description using
weight and postmenstrual age. Pediatr Nephrol. 2008

Schwartz GJ. Does kL/PCr estimate GFR, or does GFR determine k? Pediatr
Nephrol. 1992;6(6):512-5.

Matthews I, Kirkpatrick C, Holford N. Quantitative justification for
target concentration intervention -- parameter variability and
predictive performance using population pharmacokinetic models for
aminoglycosides. Br J Clin Pharmacol. 2004;58(1):8-19.

Holford N, Sherwin CM. Scaling renal function in neonates and infants to
describe the pharmacodynamics of antibiotic nephrotoxicity. PAGE 26
Abstr 7208 [wwwpage-meetingorg/?abstract=7208]. 2017.

On 06-Dec-17 23:52, R.terHeine
> Hi Ruben,
> Interesting work, Ruben. One may indeed question the validity of
> glomerular filtration rate markers like cystatin C (that is only
> filtrated and not actively secreted) to predict PK of drugs that
> undergo active tubular secretion in patients with decreased renal
> function. When glomerular filtration rate drops, the relative
> contribution of active tubular secretion to renal clearance increases.
> To me, it appears logical that creatinine is a better marker for
> clearance drugs that are actively secreted, as creatinine also
> undergoes active tubular secretion.
> Nonetheless, Im also interested whether other people have considered
> allometric scaling of MDRD/CKD-EPI derived GFRs?
> Cheers,
> Rob
> *Van: *Ruben Faelens <ruben.faelens
> *Datum: *dinsdag 5 december 2017 om 7:13 PM
> *Aan: *"Heine, Rob ter" <R.terHeine
> *CC: *"nmusers
> *Onderwerp: *Re: [NMusers] Allometric scaling of renal clearance with
> estimated glomerular filtration rate
> Dear Rob,
> At PMX Benelux, there was an interesting talk about the correlation
> between different metrics describing renal function by Stijn Jonckheere.
> A part of the work presented was published:
> <>
> This may provide some perspective, or rather complicate things even
> more, depending on your viewpoint.
> Best regards
> Ruben Faelens
On 06-Dec-17 06:17, R.terHeine
> Dear all,
> I am wondering what your thoughts are on the allometric scaling of
> clearance of renally extreted drugs, where we have estimations renal
> function.
> Simply scaling the predicted glomerular filtration rate from, for
> example, the Cockroft-gault equation seems inappropriate, since weight
> is already a part of the equation. Standardizing this to weight in the
> Cockroft-gault equation can be done, a solution has been discussed
> here:
> However, in the recent years some new equations to calculate
> glomerular filtration rate from endogenous markers have emerged. For
> example the CKD-EPI CREATININE CYSTATIN C equation
> . As the addition of a muscle mass independent endogenous marker like
> cystatin C is known to provide better estimations of GFR in, for
> example, cachectic patients, it is likely that this equation may
> outperform to predict renally filtrated compounds in this patient
> group. It is rather odd that this CKD-EPI equation does not contain
> any measure of body size. The outcome of this equation is a GFR scaled
> to a BSA of 1.73m^2.
> I am wondering how you would allometrically scale the eGFRs from these
> CKD EPI equations to, for example, fat-free mass.
> Cheers!
> Rob
> R. ter Heine, PhD, PharmD
> Hospital Pharmacist-Clinical Pharmacologist
> Radboudumc, Nijmegen, The Netherlands
> Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het
> handelsregister onder nummer 41055629.
> The Radboud university medical center is listed in the Commercial
> Register of the Chamber of Commerce under file number 41055629.

Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
office:+64(9)923-6730 mobile:NZ+64(21)46 23 53 FR+33(6)62 32 46 72
Read the question, answer the question, attempt all questions

Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het hande=
lsregister onder nummer 41055629.
The Radboud university medical center is listed in the Commercial Register =
of the Chamber of Commerce under file number 41055629.


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Received on Thu Dec 07 2017 - 08:00:51 EST

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