NONMEM Users Network Archive

Hosted by Cognigen

[NMusers] Renal function as a covariate

From: Nick Holford <>
Date: Mon, 26 Aug 2013 17:25:49 +0200


I agree with you that what I wrote was not properly explained. Thanks
for pointing this out. My previous comment was related to a question
about time-varying covariates. You raise other important issues about
how to use renal function as a covariate so I have re-named this thread
and offer the following explanation.

CLCR, as I proposed using it, should be a size standardized value -- I
should have used the term CLCRstd to make this clearer.

I suggest standardizing a prediction, such as that obtained from the
Cockcroft & Gault formula (CLCRCG), to a standard size of 70 kg as follows:


then using it as I proposed in the equation below. Note that WT is total
body weight when used with CLCRCG because this formula was developed
based on creatinine production rate expressed per kg of total body weight.

f(age) is an empirical function centered on an age of 40 years. It is of
exponential form to avoid extrapolation to negative values.
f(renal_function) is CLCRstd/100 where 100 mL/min is a 'normal' CLCR for
a 70 kg person. The model assumes CLrenal is linearly related to renal
function but more complex models can easily be implemented.

CL=(CLnon-renal*f(age) + CLrenal * f(renal_function) )
* allometric WT
CL=(THETA(1) *EXP(THETA(2)*(AGE-40)) + THETA(3) * CLCRstd/100
) * (WT/70)**0.75

This approach applies size standardization consistently to both
non-renal and renal components of clearance (see for example Mould et
al. 2002, Matthews et al. 2006 for applications).

There is a problem with the method you propose of using non-size
standardized CLCR to account for a component of clearance. Even if there
is no renal elimination of a drug, then if there is a reasonable
distribution of size in the sample being studied, then THETA(3) may
appear to be different from zero because it reflects differences in size
not just renal function.

Note that using surface area as a form of size standardization for
glomerular filtration rate has no theoretical nor experimental support
when compared to theory based allometry (Rhodin et al. 2009). So I do
not 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done but in fact this is just based on tradition and an out of date
theory of scaling based on surface area (see Anderson & Holford 2008).
The MDRD method of predicting glomerular filtration rate is a
statistical absurdity which does not include any measurement of size for
its prediction. I would certainly not recommend using it for any
scientific purpose.

The choice of units for CLCR is somewhat context dependent. The commonly
used Cockcroft & Gault method (CLCRCG) returns values in mL/min so that
is why I chose 100 mL/min for a 70 kg person. I would agree that in
general it is better to report clearances as L/h/70kg.

Describing CLCR as 'renal function' is also traditional but I prefer to
calculate the ratio of the predicted CLCRstd in an individual to a
standard 'normal' value to obtain a dimensionless renal function
variable that is independent of size and is more directly related to the
function of the kidneys. This renal function value also gets around the
problems of units chosen to express CLCR as long as consistent values
are chosen to compare the individual prediction with the 'normal' value.

Please look at this recent review of the use of standards for PK
Parameters which discusses this issue and also demonstrates how to
account for maturation of renal functionfor ages less than 2 years
(Holford, Yeo, Anderson 2013).

Best wishes,


1. Mould DR, Holford NH, Schellens JH, Beijnen JH, Hutson PR, Rosing
H, et al. Population pharmacokinetic and adverse event analysis of
topotecan in patients with solid tumors. Clinical Pharmacology &
Therapeutics. 2002;71(5):334-48.
2. 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.
3. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole
M, et al. Human renal function maturation: a quantitative description
using weight and postmenstrual age. Pediatr Nephrol. 2009;24(1):67-76.
4. Anderson BJ, Holford NH. Mechanism-based concepts of size and
maturity in pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32.
5. Holford N, Heo YA, Anderson B. A pharmacokinetic standard for
babies and adults. J Pharm Sci. 2013;102(9):2941-52.

On 26/08/2013 4:09 p.m., J.H. Proost wrote:
> Dear Nick,
> In your reply to Siwei, you proposed the following code:
>> $PK
>> ; CL=(CLnon-renal*f(age) + CLrenal*f(renal_function)) * allometric WT
>> CL=(THETA(1)*EXP(THETA(2)*(AGE-40)) + THETA(3)*CLCR/100)*(WT/70)**0.75
> I would like to make a comment on the coding of the renal function. If
> CLCR is expressed in ml/min, the expression THETA(3)*CLCR/100
> represents the renal clearance of the individual with renal function
> CLCR, where THETA(3) is the drug's renal clearance for an individual
> with creatinine clearance of 100 ml/min (a reasonable value for an
> average individual but not a standard value).
> In my opinion, the allometric term should not be applied on this renal
> part of clearance. Therefore I suggest to use the following code line:
> ; CL= CLnon-renal*f(age)*allometric WT + CLrenal*f(renal_function)
> CL= THETA(1)*EXP(THETA(2)*(AGE-40))*(WT/70)**0.75 + THETA(3)*CLCR/100
> If CLCR is expressed in ml/min/1.73m2 (the 'normalized renal
> function', often used in lab results, e.g. in the MDRD equation;
> useful for clinical judgement of renal function, but not for modeling
> or dosing purposes), your code could be used, but in that case I would
> prefer to first convert CLCR to ml/min (the 'true renal function') and
> then use the above code line.
> Note: Units of THETA(1) and THETA(3) are here in ml/min; for using the
> more conventional L/h, multiplication by 60/1000 should be added.
> best regards,
> Hans Proost
> Johannes H. Proost
> Dept. of Pharmacokinetics, Toxicology and Targeting
> University Centre for Pharmacy
> Antonius Deusinglaan 1
> 9713 AV Groningen, The Netherlands
> tel. 31-50 363 3292
> fax 31-50 363 3247
> Email:

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(7)85 36 84 99

Holford NHG. Disease progression and neuroscience. Journal of Pharmacokinetics and Pharmacodynamics. 2013;40:369-76
Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and adults. J Pharm Sci. 2013:
Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. 2013;2:
Holford NHG. Clinical pharmacology = disease progression + drug action. British Journal of Clinical Pharmacology. 2013:

Received on Mon Aug 26 2013 - 11:25:49 EDT

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to: Once subscribed, you may contribute to the discussion by emailing: