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Re: [FORGED] [NMusers] Allometric scaling of renal clearance with estimated glomerular filtration rate

From: Nick Holford <>
Date: Thu, 7 Dec 2017 08:05:30 +1300

Hi Rob,

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

1. Theory Based Allometry or Surface Area

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

There is no biological or experimental support for using surface area to
scale renal function markers such as GFR and CLcr.  In contrast, there
is strong 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 absurdity 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
serum creatiniine. This is based on the definition of clearance and is
true without any assumptions.
If we then assume Scr is at steady state then CER will be equal to
creatinine production rate (CPR) and we can use this:
All rational models for predicting CLcr without measurement of CER use
models to predict CPR e.g.

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

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

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

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

So what to do?

First -- don't use MDRD or CKI-EPI unless you are sure you are applying
them to a population similar to that used to develop these empirical
predictions. You could add allometric scaling to the eGFR by assuming
the 1.72m^2 value 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
then the Matthews (2004) equation for adults. I am working on an
integrated method 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
0.993^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
(standardized 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, wrote:
> 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, I’m also interested whether other people have considered
> allometric scaling of MDRD/CKD-EPI derived GFR’s?
> Cheers,
> Rob
> *Van: *Ruben Faelens <>
> *Datum: *dinsdag 5 december 2017 om 7:13 PM
> *Aan: *"Heine, Rob ter" <>
> *CC: *"" <>
> *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, wrote:
> 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

Received on Wed Dec 06 2017 - 14:05:30 EST

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