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Re: Schwartz formulae

From: Nick Holford <n.holford>
Date: Wed, 01 Apr 2009 08:42:57 +0200

Mahesh, Samer,

The Schwartz formulae are based on theoretical allometric principles.
The allometric theory is based on the assumption that creatinine
production rate (CPR) is proportional to body surface area. Other
possibilities exist e.g. that CPR is directly proportional to body mass.
It is usually assumed that CPR is proportional to muscle mass.
Theoretical allometry (West et al. 1999) would suggest that a structural
feature such as muscle mass would be best described by an allometric
coefficient of 1. Putting these two assumptions together would indicate
that CPR and body mass should be related linearly. This is the
assumption made in the Cockcroft & Gault formula. Part of the need to
change 'k' for different sizes of children may be due to choosing the
wrong allometric model.

The Schwartz formula coefficient 'k' has various empirically determined
values depending on age and sex. This means that the original allometric
theory has been discarded in favour of empirical allometry. Theoretical
allometry is primarily concerned with the relationship between body size
and body structure or function. Other things such as age and sex can of
course be important to describe how muscle mass and thus CPR may differ
between people. But these other factors should be considered in addition
to the fundamental allometric method and not used to distort it. The
changing values of 'k' in the various Schwartz formulae are a
consequence of this ad hoc approach.

It should also be noted that the Schwartz formulae are designed to
predict creatinine clearance (CLcr). In children with more or less
normal renal function the Schwartz predicted CLcr is 30% greater than
concurrently measured inulin clearance (a 'gold standard' GFR estimation
method) (see Hellerstein et al 1992). This is different from adults in
whom GFR and CLcr are very similar.


Hellerstein S, Alon U, Warady BA. Creatinine for estimation of
glomerular filtration rate. Pediatr Nephrol. 1992;6:507-11.

West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal
geometry and allometric scaling of organisms. Science.

Mouksassi Mohamad-Samer wrote:
> Dear Mahesh,
> As any model the original equation of Schwartz is evolving over the years and as more data is gathered.
> The original paper had only one k :
> Schwartz GJ, Haycock GB, Edelmann CM Jr, Spitzer A. A simple estimate of glomerular filtration rate in children derived from body length and plasma creatinine. Pediatrics 1976; 58:259–263.
> Then it was extended to other age groups to account for the maturational changes:
> Schwartz GJ, Brion LP, Spitzer A. The use of plasma creatinine concentration for estimating glomerular filtration rate in infants, children, and adolescents. Pediatr Clin North Am 1987; 34:571–590.
> Then other papers suggested different adjustment to the original formula... and to make it applicable for other age groups.
> Please also note that the original k are applicable only for the old/standard Jaffe method to measure serum creatinine.
> Newer methods require some adjustments.
> Newer formulas are now published using cystatin and other markers.
> Zappitelli M, Parvex P, Joseph L, et al. Derivation and validation of cystatin
> C-based prediction equations for GFR in children. Am J Kidney Dis 2006;
> 48:221–230
> (standard Schwartz formula may be misleading when we have renal impairment)
> New equations to estimate GFR in children with CKD.
> Schwartz GJ, Muñoz A, Schneider MF, Mak RH, Kaskel F, Warady BA, Furth SL.
> J Am Soc Nephrol. 2009 Mar;20(3):629-37. Epub 2009 Jan 21.
> Estimating and measuring glomerular filtration rate in children.
> Work DF, Schwartz GJ.
> Curr Opin Nephrol Hypertens. 2008 May;17(3):320-5. Review.
> The right formula will depend on the nature of your pediatric population you want to calculate CRCL for , the method used for serum creatinine and whether you have some renally impaired children or not.
> Hope this helps
> Samer
> -----Original Message-----
> From: owner-nmusers
> Sent: Tue 3/31/2009 16:09
> To: nmusers
> Subject: [NMusers] Schwartz formulae
> Dear NMusers,
> I am having difficulty with the Schwartz formulae for computing GFR in kids. Some references state that the formula gives GFR in mL/min while others say it is mL/min/1.73 m². Also the value of k varies between references. This is what I plan on using. Are these formulas in the right units with the correct constants.
> Please advise,
> Mahesh
> ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*
> Schwartz formula:
> GFR (mL/min/1.73 m²) = k*Height(cm) / Serum Creatinine (mg/dL)
> k = 0.33 in Preterm Infants
> k = 0.45 in Term infants to 1 year old
> k = 0.55 for children aged 2 to 12 years
> k = 0.55 for girls 13 to 21 years, and
> k = 0.70 for boys 13 to 21 years
> GFR corrected for the child's actual BSA, which can be obtained using the DuBois and DuBois formula
> GFR corrected = [GFR * 1.73] / BSA
> The DuBois and DuBois formula:
> BSA (m²) = (Weight^0.425 x Height^0.725) x 0.007184
> where the weight is in kilograms and the height is in centimeters.
> ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*

Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
Received on Wed Apr 01 2009 - 02:42:57 EDT

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