

Journal of the New Zealand Medical Association, 24February2012, Vol 125 No 1350 

The Cockroft and Gault formula for estimation of
creatinine clearance: a friendly deconstruction
J Alasdair Millar
The Cockroft and Gault formula for estimating creatinine
clearance (CCr) as a proxy for glomerular
filtration rate (GFR) has been in use for clinical and research purposes since
its derivation in 1976.1 Recently it has been
largely superceded by the eGFR, based on the MDRD formula
[, (omitting factors for sex and race)]
but remains a valuable bedside tool for estimating the need to adjust the doses
of drugs that are cleared by the kidney in patients with renal
dysfunction.2
In this paper I review the derivation of the Cockroft and
Gault formula from a historical perspective and comment on its use at the
bedside.
MethodsThis work is based on an analysis of the paper by
Donald W Cockroft and M Henry Gault in Nephron
(1976)1 and some extrapolations therefrom. The
formula as published was
(Equation 1). An alternative formula without weight as
a dependent variable was derived from the paper after calculating total 24 hr
creatinine excretion, following the method described by Cockroft and
Gault.
Derivation of the formula:
Cockroft and Gault studied 534 consecutive patients in
whom creatinine clearance was measured on 2 or more occasions using serum and
24hour urine creatinine concentrations. Ninety six percent of the patients were
male. Patients (n = 29) were excluded if not in steady state (blood creatinine
values differed by > 20%). A subgroup (“Group II”) used for the
derivation of the formula (n = 236) was formed from “Group I” by
further excluding patients whose 24hr urine creatinine values differed by more
than 20% (n = 173) or was < 10 mg/Kg (n = 31) or where the records were
inadequate (n = 65). Group II was augmented by reinclusion of 23 patients who
satisfied the second criteria but whose 24hr urine volume was > 500 ml
(final n = 249).
The steps in deriving the formula
were:
Step 1. The relationship between
creatinine excretion expressed as mg/kg/24h (as the dependent variable)
(CrUV24/kg) was plotted against age (independent variable) after aggregating
data into age bands of 10 years (data given as table II in their paper).
Step 2. The equation for the curve was
obtained by linear regression:
(Equation
2)
Step 3. Both sides of the equation
were multiplied by weight, to give
(Equation
3)
Step 4. Equation 3 for CrUV24 (mg) was
inserted into the expression for creatinine clearance and hence the final
equation was derived:
Cockcroft and Gault validated their formula by
comparing it to three other formulae35 for
creatinine clearance and against a nomogram published from
Denmark,6 which contained body weight. Cockroft
and Gault noted that as the average weight in their Group II was 72 kg, their
formula simplified to for patients of
average weight.
Comment and discussionFrom a modern perspective, several aspects of the derivation
of the Cockroft and Gault formula require comment.
It is
possible to derive a valid equation from the Cockroft and Gault data that does
not depend on weight, by calculation of the 24 hr urine creatinine according to
each age group assuming that the average weight applies throughout, and using
these data to follow the stepwise procedure used by the authors.
The new data are:
Regressing CrUV (mg/24 h) on weight gives the linear
equation
(Compare with
equation 2 above). When this equation is substituted into the equation for
creatinine clearance, the result after collection of terms becomes
, or in SI units,
(Equation 4). This is almost identical
to the Cockroft and Gault formula when it is applied to patients of average
weight, but this is to be expected since the derivation involved using the
constant factor, equal to average weight, of 72. I did not study the performance
of this formula in detail and mention it here only to emphasize the
circumstances surrounding the inclusion of body weight in the Cockroft and Gault
formula. However, it is of interest that body weight was not a significant
independent variable in the derivation of eGFR using the MDRD Study patients.
Because 96% of Cockroft and Gault’s patients were
male, the original formula applies only to male patients. The creatinine
clearance in females is about 85% of males. Hence the use of the formula at the
bedside is greatly simplified if the factor of 1.23 in equation 1 is ignored and
the result is regarded as the value of CLCr in
females. For a male patient, simply add 20%.
ConclusionThe Cockroft and Gault formula has stood the test of time
and hence may be said to have been validated by usage. However, its derivation
was unusual and involved circular logic. The introduction of the weight variable
appears to have come from an arbitrary regression of 24 hr creatinine excretion
(as mg/kg) on age, with a subsequent manipulation that caused body weight to
appear as an independent variable in the published formula.
With the possible exception of formula
III,5 all the preexisting formulae for
creatinine clearance listed by Cockroft and Gault gave usable values, as does
Equation 4 above (results not shown). Thus it appears that there are a range of
potentially usable formulae for CCr that are reciprocal functions of serum
creatinine but vary in the other dependent variables and scaling factors. This
is confirmed by the example of the eGFR equation in which the term
.
Historical noteProfessor Cockroft graduated in medicine at the University
of British Columbia in 1950. He now works as a researcher in asthma at the
Department of Medicine, University of Saskatchewan in Saskatoon. His career has
taken him there via San Jose, Montreal, Vancouver and Hamilton (Ontario).
This author approached Professor Cockcroft at his place of
work and requested clarification on the reason for including weight in the
regression equation. Professor Cockcroft replied that the primary interest of
the work was effectively to validate the values for
CLCr obtained from the Danish
nomogram,6 which contains weight, but he could
not recall the specific reason for the choice of regression. In the event, his
objective was secured (see Cockroft and Gault, Table III).
Professor Gault died in May 2003. His obituary from the
University of Newfoundland9 describes him as a
pioneer in the field of nephrology. As a young man he survived 31 wartime
bombing missions over Germany with the Royal Canadian Air Force. His subsequent
nephrology career was in Montreal and Newfoundland.
Competing interests: None
declared.
Author information: J Alasdair Millar,
Consultant Physician and Clinical Director, Medical Department, Southland
Hospital, Invercargill.
Correspondence: J Alasdair Millar,
Consultant Director Acute Care Services, Albany Regional Hospital, Warden Ave,
Albany, WA 6330, Australia. Email Alasdair.millar@health.wa.gov.au
References:


Current
issue  Search journal 
Archived issues  Classifieds
 Hotline (free ads) Subscribe  Contribute  Advertise  Contact Us  Copyright  Other Journals 