Dear All,
I have enjoyed the recent discussions on time-varying covariates and renal
function as a covariate. The two topics emerged from a single thread. Not
to belabor this, but I thought it interesting to bring these back together
in order to pose a question. How would one deal with renal function and
"size" as time varying covariates if administration of the drug in question
results in changes in weight over time?
Kind regards,
Matt
Time-varing covariate and renal function as a covariate
Dear Matt,
I'm not quite sure that I fully understand your question. I would say that a
changing renal function and a changing weight over time can be handled as
described earlier by Nick Holford, or by the modified approach I suggested. An
important point is how to express renal function.
Nick's method implies that 'size' should be excluded from 'renal function', so
CLCR needs to be normalized / standardized, e.g. using CLCR in ml/min/1.73m2.
Now, CLCR is a 'pure' measure of the kidney function (of course, we know that
its precision is rather poor, but that is a different topic, interesting as
well!). The factor WEIGHT^0.75 deals with the factor 'size'. This approach
treats CLCR as a covariate similar to other covariates, making it more suitable
for a standardized approach for covariate analysis.
In the approach proposed by me, CLCR should be the 'individual's renal
clearance of creatinine', so it should expressed in ml/min (or converted to
e.g. l/h), and it should not be normalized / standardized. Here, CLCR includes
both kidney function and size (in Nick's view a disadvantage, in my view an
advantage), and the renal part of the equation does not need further
modification to take 'size' into account. This approach treats CLCR as a
'special' covariate, directly related to the renal clearance of the drug. This
may be advantageous for clinical purposes, e.g. dose calculation and
therapeutic drug monitoring.
In my view, both approaches have advantages and disadvantages.
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: [email protected]
----- Original Message -----
Quoted reply history
From: Matt Hutmacher
To: 'nmusers'
Sent: Thursday, August 29, 2013 5:03 PM
Subject: [NMusers] Time-varing covariate and renal function as a covariate
Dear All,
I have enjoyed the recent discussions on time-varying covariates and renal
function as a covariate. The two topics emerged from a single thread. Not to
belabor this, but I thought it interesting to bring these back together in
order to pose a question. How would one deal with renal function and "size" as
time varying covariates if administration of the drug in question results in
changes in weight over time?
Kind regards,
Matt
Matt,
Thanks for your interest in this question. Hans and I have differing approaches for including 'renal function' but I think we agree on 'size'. Our differences of approach to 'renal function' are not very important for those who understand the biology and pharmacology. But its different when we have to talk to statisticians.
While I recognize that you are not typical of statisticians (you know something about biology and pharmacology) it would help me (and probably Hans) if you stated more precisely what you mean by 'renal function' and 'size' and why you think there is a challenge if weight changes over time?
Best wishes,
Nick
Quoted reply history
On 2/09/2013 9:04 a.m., J.H. Proost wrote:
> Dear Matt,
>
> I'm not quite sure that I fully understand your question. I would say that a changing renal function and a changing weight over time can be handled as described earlier by Nick Holford, or by the modified approach I suggested. An important point is how to express renal function. Nick's method implies that 'size' should be excluded from 'renal function', so CLCR needs to be normalized / standardized, e.g. using CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney function (of course, we know that its precision is rather poor, but that is a different topic, interesting as well!). The factor WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as a covariate similar to other covariates, making it more suitable for a standardized approach for covariate analysis. In the approach proposed by me, CLCR should be the 'individual's renal clearance of creatinine', so it should expressed in ml/min (or converted to e.g. l/h), and it should not be normalized / standardized. Here, CLCR includes both kidney function and size (in Nick's view a disadvantage, in my view an advantage), and the renal part of the equation does not need further modification to take 'size' into account. This approach treats CLCR as a 'special' covariate, directly related to the renal clearance of the drug. This may be advantageous for clinical purposes, e.g. dose calculation and therapeutic drug monitoring.
>
> In my view, both approaches have advantages and disadvantages.
> 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: [email protected] <mailto:[email protected]>
>
> ----- Original Message -----
> *From:* Matt Hutmacher <mailto:[email protected]>
> *To:* 'nmusers' <mailto:[email protected]>
> *Sent:* Thursday, August 29, 2013 5:03 PM
> *Subject:* [NMusers] Time-varing covariate and renal function as a
> covariate
>
> Dear All,
>
> I have enjoyed the recent discussions on time-varying covariates
> and renal function as a covariate. The two topics emerged from a
> single thread. Not to belabor this, but I thought it interesting
> to bring these back together in order to pose a question. How
> would one deal with renal function and “size” as time varying
> covariates if administration of the drug in question results in
> changes in weight over time?
>
> Kind regards,
>
> Matt
--
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
email: [email protected]
http://holford.fmhs.auckland.ac.nz/
Holford NHG. Disease progression and neuroscience. Journal of Pharmacokinetics
and Pharmacodynamics. 2013;40:369-76
http://link.springer.com/article/10.1007/s10928-013-9316-2
Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and
adults. J Pharm Sci. 2013:
http://onlinelibrary.wiley.com/doi/10.1002/jps.23574/abstract
Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. 2013;2:
http://www.nature.com/psp/journal/v2/n5/full/psp201318a.html
Holford NHG. Clinical pharmacology = disease progression + drug action. British
Journal of Clinical Pharmacology. 2013:
http://onlinelibrary.wiley.com/doi/10.1111/bcp.12170/abstract
Hello Nick, Hans
Thanks for the replies and sorry for being so vague. I wanted to get your
opinions about such a scenario without providing information that might
"steer" the dialogue.
Perhaps a hypothetical will help clarify my scientific curiosity. Let's say
at baseline we take measurements of weight (WT), etc. Assume
Cockcroft-Gault is used to predict CLCR. We formulate a model either by
Nick's or Hans' method below to relate WT and CLCR (a function of WT) to CL
of the drug. However, over time, the drug changes WT... in some way the
ratio of fat to lean mass is altered by the drug. Should we expect the same
structural relationship to hold as we would have assumed at baseline (before
we knew the drug changes WT)? And if so, then should we assume the same
coefficients (exponents) for CLCR and WT would hold over time in such a
model, such that just adjusting CLCR and WT as time varying covariates is
all that is needed to be predictive? As another example, let's assume we do
a pooled population PK using healthy volunteers and obese patients. Then,
say a drug is administered that reduces WT. Should we use the same exponent
(coefficient) for healthy volunteers and obese patients? And if the drug
works, should at what point should we treat the obese patients as healthy
volunteers - or would just using WT and CLCR take care of it?.
Best regards,
Matt
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Nick Holford
Sent: Monday, September 02, 2013 12:16
To: 'nmusers'
Subject: Re: [NMusers] Time-varing covariate and renal function as a
covariate
Matt,
Thanks for your interest in this question. Hans and I have differing
approaches for including 'renal function' but I think we agree on 'size'.
Our differences of approach to 'renal function' are not very important for
those who understand the biology and pharmacology. But its different when we
have to talk to statisticians.
While I recognize that you are not typical of statisticians (you know
something about biology and pharmacology) it would help me (and probably
Hans) if you stated more precisely what you mean by 'renal function' and
'size' and why you think there is a challenge if weight changes over time?
Best wishes,
Nick
On 2/09/2013 9:04 a.m., J.H. Proost wrote:
> Dear Matt,
> I'm not quite sure that I fully understand your question. I would say
> that a changing renal function and a changing weight over time can be
> handled as described earlier by Nick Holford, or by the modified
> approach I suggested. An important point is how to express renal
> function.
> Nick's method implies that 'size' should be excluded from 'renal
> function', so CLCR needs to be normalized / standardized, e.g. using
> CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney
> function (of course, we know that its precision is rather poor, but
> that is a different topic, interesting as well!). The factor
> WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as
> a covariate similar to other covariates, making it more suitable for a
> standardized approach for covariate analysis.
> In the approach proposed by me, CLCR should be the 'individual's renal
> clearance of creatinine', so it should expressed in ml/min (or
> converted to e.g. l/h), and it should not be normalized /
> standardized. Here, CLCR includes both kidney function and size (in
> Nick's view a disadvantage, in my view an advantage), and the renal
> part of the equation does not need further modification to take 'size'
> into account. This approach treats CLCR as a 'special' covariate,
> directly related to the renal clearance of the drug. This may be
> advantageous for clinical purposes, e.g. dose calculation and
> therapeutic drug monitoring.
> In my view, both approaches have advantages and disadvantages.
> 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: [email protected] <mailto:[email protected]>
>
Dear Matt,
Your first hypothetical scenario is an argument not to use CRCL because as you
point out, weight is entering the model twice: once to predict renal function
and once to scale for size. Other problems of using models that predict CLCr
(when really you are interested in your drug CL, not the CL of endogenous
creatinine) is that they are only valid for certain populations so if you have
say adults and children in your dataset, at what point do you switch between
C-G and the Schwartz method? Perhaps a better way is to scale clearance with
measured creatinine normalised to the age-adjusted value (which if your drug is
renally cleared to any extent should be correlated in some way), and then have
a separate weight scaling - that way age, weight and SeCr all only enter into
the model once, and can be updated as often as they are measured for
time-varying techniques. You can then try different metrics for weight if you
have some obese subjects (FFM, LBW...). This approach has been used a couple
of times:
Johansson ÅM et al. TDM. 2011;33(6):711-8.
Germovsek E et al. Age-Corrected Creatinine is a Significant Covariate for
Gentamicin Clearance in Neonates. PAGE 2013.
BW,
Joe
Joseph F Standing
MRC Fellow, UCL Institute of Child Health
Antimicrobial Pharmacist, Great Ormond Street Hospital
Tel: +44(0)207 905 2370
Mobile: +44(0)7970 572435
Quoted reply history
________________________________________
From: [email protected] [[email protected]] On Behalf Of
Matt Hutmacher [[email protected]]
Sent: 03 September 2013 18:00
To: 'Nick Holford'; 'nmusers'
Subject: RE: [NMusers] Time-varing covariate and renal function as a covariate
Hello Nick, Hans
Thanks for the replies and sorry for being so vague. I wanted to get your
opinions about such a scenario without providing information that might
"steer" the dialogue.
Perhaps a hypothetical will help clarify my scientific curiosity. Let's say
at baseline we take measurements of weight (WT), etc. Assume
Cockcroft-Gault is used to predict CLCR. We formulate a model either by
Nick's or Hans' method below to relate WT and CLCR (a function of WT) to CL
of the drug. However, over time, the drug changes WT... in some way the
ratio of fat to lean mass is altered by the drug. Should we expect the same
structural relationship to hold as we would have assumed at baseline (before
we knew the drug changes WT)? And if so, then should we assume the same
coefficients (exponents) for CLCR and WT would hold over time in such a
model, such that just adjusting CLCR and WT as time varying covariates is
all that is needed to be predictive? As another example, let's assume we do
a pooled population PK using healthy volunteers and obese patients. Then,
say a drug is administered that reduces WT. Should we use the same exponent
(coefficient) for healthy volunteers and obese patients? And if the drug
works, should at what point should we treat the obese patients as healthy
volunteers - or would just using WT and CLCR take care of it?.
Best regards,
Matt
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Nick Holford
Sent: Monday, September 02, 2013 12:16
To: 'nmusers'
Subject: Re: [NMusers] Time-varing covariate and renal function as a
covariate
Matt,
Thanks for your interest in this question. Hans and I have differing
approaches for including 'renal function' but I think we agree on 'size'.
Our differences of approach to 'renal function' are not very important for
those who understand the biology and pharmacology. But its different when we
have to talk to statisticians.
While I recognize that you are not typical of statisticians (you know
something about biology and pharmacology) it would help me (and probably
Hans) if you stated more precisely what you mean by 'renal function' and
'size' and why you think there is a challenge if weight changes over time?
Best wishes,
Nick
On 2/09/2013 9:04 a.m., J.H. Proost wrote:
> Dear Matt,
> I'm not quite sure that I fully understand your question. I would say
> that a changing renal function and a changing weight over time can be
> handled as described earlier by Nick Holford, or by the modified
> approach I suggested. An important point is how to express renal
> function.
> Nick's method implies that 'size' should be excluded from 'renal
> function', so CLCR needs to be normalized / standardized, e.g. using
> CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney
> function (of course, we know that its precision is rather poor, but
> that is a different topic, interesting as well!). The factor
> WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as
> a covariate similar to other covariates, making it more suitable for a
> standardized approach for covariate analysis.
> In the approach proposed by me, CLCR should be the 'individual's renal
> clearance of creatinine', so it should expressed in ml/min (or
> converted to e.g. l/h), and it should not be normalized /
> standardized. Here, CLCR includes both kidney function and size (in
> Nick's view a disadvantage, in my view an advantage), and the renal
> part of the equation does not need further modification to take 'size'
> into account. This approach treats CLCR as a 'special' covariate,
> directly related to the renal clearance of the drug. This may be
> advantageous for clinical purposes, e.g. dose calculation and
> therapeutic drug monitoring.
> In my view, both approaches have advantages and disadvantages.
> 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: [email protected] <mailto:[email protected]>
>
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Hi Matt and Everyone,
Whether or not "just using weight and CLCR should be enough" depends on whether
you think that people who lost weight because of a drug (the formerly obese)
are physilogically the same (with respect to the drugs in question) as those
who were never obese. Are the formerly-obese maybe even a third group,
different from non-obese and currently-obese?
That said, making a distinction between healthy vs obese is odd. Obesity is a
continuum and there shouldn't be model discontinuity when someone meets some
arbitrary criteria. There shouldn't be choice "obese vs. non-obese", everything
just comes as a smooth function of the covariates. Nature is "smooth" and, if
possible, our models should be too.
Warm regards,
Douglas Eleveld
-----Oorspronkelijk bericht-----
Quoted reply history
Van: [email protected] [mailto:[email protected]] Namens
Matt Hutmacher
Verzonden: September 3, 2013 7:00 PM
Aan: 'Nick Holford'; 'nmusers'
Onderwerp: RE: [NMusers] Time-varing covariate and renal function as a covariate
Hello Nick, Hans
Thanks for the replies and sorry for being so vague. I wanted to get your
opinions about such a scenario without providing information that might "steer"
the dialogue.
Perhaps a hypothetical will help clarify my scientific curiosity. Let's say at
baseline we take measurements of weight (WT), etc. Assume Cockcroft-Gault is
used to predict CLCR. We formulate a model either by Nick's or Hans' method
below to relate WT and CLCR (a function of WT) to CL of the drug. However,
over time, the drug changes WT... in some way the ratio of fat to lean mass is
altered by the drug. Should we expect the same structural relationship to hold
as we would have assumed at baseline (before we knew the drug changes WT)? And
if so, then should we assume the same coefficients (exponents) for CLCR and WT
would hold over time in such a model, such that just adjusting CLCR and WT as
time varying covariates is all that is needed to be predictive? As another
example, let's assume we do a pooled population PK using healthy volunteers and
obese patients. Then, say a drug is administered that reduces WT. Should we
use the same exponent
(coefficient) for healthy volunteers and obese patients? And if the drug
works, should at what point should we treat the obese patients as healthy
volunteers - or would just using WT and CLCR take care of it?.
Best regards,
Matt
-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Nick Holford
Sent: Monday, September 02, 2013 12:16
To: 'nmusers'
Subject: Re: [NMusers] Time-varing covariate and renal function as a covariate
Matt,
Thanks for your interest in this question. Hans and I have differing approaches
for including 'renal function' but I think we agree on 'size'.
Our differences of approach to 'renal function' are not very important for
those who understand the biology and pharmacology. But its different when we
have to talk to statisticians.
While I recognize that you are not typical of statisticians (you know something
about biology and pharmacology) it would help me (and probably
Hans) if you stated more precisely what you mean by 'renal function' and 'size'
and why you think there is a challenge if weight changes over time?
Best wishes,
Nick
On 2/09/2013 9:04 a.m., J.H. Proost wrote:
> Dear Matt,
> I'm not quite sure that I fully understand your question. I would say
> that a changing renal function and a changing weight over time can be
> handled as described earlier by Nick Holford, or by the modified
> approach I suggested. An important point is how to express renal
> function.
> Nick's method implies that 'size' should be excluded from 'renal
> function', so CLCR needs to be normalized / standardized, e.g. using
> CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney
> function (of course, we know that its precision is rather poor, but
> that is a different topic, interesting as well!). The factor
> WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as
> a covariate similar to other covariates, making it more suitable for a
> standardized approach for covariate analysis.
> In the approach proposed by me, CLCR should be the 'individual's renal
> clearance of creatinine', so it should expressed in ml/min (or
> converted to e.g. l/h), and it should not be normalized /
> standardized. Here, CLCR includes both kidney function and size (in
> Nick's view a disadvantage, in my view an advantage), and the renal
> part of the equation does not need further modification to take 'size'
> into account. This approach treats CLCR as a 'special' covariate,
> directly related to the renal clearance of the drug. This may be
> advantageous for clinical purposes, e.g. dose calculation and
> therapeutic drug monitoring.
> In my view, both approaches have advantages and disadvantages.
> 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: [email protected] <mailto:[email protected]>
>
________________________________
Dear Matt,
I still don't see the problem you are raising. Both the approach of Nick and my
approach separate weight and CLCR as much as possible, and I don't see why this
should not work in your example. You stated:
> CLCR (a function of WT)
This is not necessarily true. It depends on whether CLCR is normalised (which
should be done that the resulting value is expected to be independent of WT) or
non-normalised (as in my approach, where CLCR is a measure of renal function
including the effect of weight). Also, the word 'function' is not correct here,
since there is no direct relationship at the individual level: it is not true
that eating will result in an increase of CLCR. However, it is true that a big
person is expected to have a higher non-normalized CLCR than a small person.
best regards,
Hans
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: [email protected] <[email protected]>
Quoted reply history
On 03-09-13, Matt Hutmacher <[email protected]> wrote:
>
> Hello Nick, Hans
>
> Thanks for the replies and sorry for being so vague. I wanted to get your
> opinions about such a scenario without providing information that might
> "steer" the dialogue.
>
> Perhaps a hypothetical will help clarify my scientific curiosity. Let's say
> at baseline we take measurements of weight (WT), etc. Assume
> Cockcroft-Gault is used to predict CLCR. We formulate a model either by
> Nick's or Hans' method below to relate WT and CLCR (a function of WT) to CL
> of the drug. However, over time, the drug changes WT... in some way the
> ratio of fat to lean mass is altered by the drug. Should we expect the same
> structural relationship to hold as we would have assumed at baseline (before
> we knew the drug changes WT)? And if so, then should we assume the same
> coefficients (exponents) for CLCR and WT would hold over time in such a
> model, such that just adjusting CLCR and WT as time varying covariates is
> all that is needed to be predictive? As another example, let's assume we do
> a pooled population PK using healthy volunteers and obese patients. Then,
> say a drug is administered that reduces WT. Should we use the same exponent
> (coefficient) for healthy volunteers and obese patients? And if the drug
> works, should at what point should we treat the obese patients as healthy
> volunteers - or would just using WT and CLCR take care of it?.
>
> Best regards,
> Matt
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> <[email protected]]> On
> Behalf Of Nick Holford
> Sent: Monday, September 02, 2013 12:16
> To: 'nmusers'
> Subject: Re: [NMusers] Time-varing covariate and renal function as a
> covariate
>
> Matt,
>
> Thanks for your interest in this question. Hans and I have differing
> approaches for including 'renal function' but I think we agree on 'size'.
> Our differences of approach to 'renal function' are not very important for
> those who understand the biology and pharmacology. But its different when we
> have to talk to statisticians.
>
> While I recognize that you are not typical of statisticians (you know
> something about biology and pharmacology) it would help me (and probably
> Hans) if you stated more precisely what you mean by 'renal function' and
> 'size' and why you think there is a challenge if weight changes over time?
>
> Best wishes,
>
> Nick
>
>
> On 2/09/2013 9:04 a.m., J.H. Proost wrote:
> > Dear Matt,
> > I'm not quite sure that I fully understand your question. I would say
> > that a changing renal function and a changing weight over time can be
> > handled as described earlier by Nick Holford, or by the modified
> > approach I suggested. An important point is how to express renal
> > function.
> > Nick's method implies that 'size' should be excluded from 'renal
> > function', so CLCR needs to be normalized / standardized, e.g. using
> > CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney
> > function (of course, we know that its precision is rather poor, but
> > that is a different topic, interesting as well!). The factor
> > WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as
> > a covariate similar to other covariates, making it more suitable for a
> > standardized approach for covariate analysis.
> > In the approach proposed by me, CLCR should be the 'individual's renal
> > clearance of creatinine', so it should expressed in ml/min (or
> > converted to e.g. l/h), and it should not be normalized /
> > standardized. Here, CLCR includes both kidney function and size (in
> > Nick's view a disadvantage, in my view an advantage), and the renal
> > part of the equation does not need further modification to take 'size'
> > into account. This approach treats CLCR as a 'special' covariate,
> > directly related to the renal clearance of the drug. This may be
> > advantageous for clinical purposes, e.g. dose calculation and
> > therapeutic drug monitoring.
> > In my view, both approaches have advantages and disadvantages.
> > 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: [email protected] <mailto:[email protected] <[email protected]>>
> >
>
>
>
Matt,
Douglas (like me) thinks about this as biological problem. I believe that 'size' is a continuum that incorporates at least some partition of weight into fat free mass (FFM) and fat mass (see Anderson & Holford 2009). The distinction between 'obese' and 'non-obese' is an artificial distinction used by health lobby groups, epidemiologists et al.
CLcr is predicted from creatinine production rate (CPR) divided by serum creatinine (Cockcroft & Gault for adults, various Schwartz methods of babies and children). CPR is predicted empirically using for age, sex and total body weight (TBW)(Schwartz uses height). Note that C&G is based on TBW. Other attempts to use IBW, LBW etc instead of TBW are imaginative at best but not based on data. Given an estimate of CPR by C&G method or by direct measurement of urinary excretion rate then CLcr can be computed under the assumption that serum creatinine (Scr) is at steady state (or with a somewhat different approach non-steady state Scr may be used). Thus the prediction of CLcr may or may not involve the use of weight. At this point it doesn't matter whether weight was used to calculate it or not. What is important is to recognize that both C&G and direct measurement both predict CLcr that is size dependent. In order to get around this confounding with allometric approaches to size you just need to standardize the CLcr to a standard weight. Then renal function can be calculated as a dimensionless quantity by dividing the weight standardized CLcr prediction by whatever CLcr you think is 'normal' for that weight. If you go through this quite simple process you can use renal function as a size independent covariate.
The time varying issue is then related to weight for calculation of CPR. If weight changes are not due to changes in muscle mass then C&G CLcr should be calculated from the baseline TBW because changes in TBW from baseline will not be associated with a change in CPR.
The time varying issue of size (e.g. based on FFM + Fat Mass) also depends on thinking about why weight is changing. If height is constant then formulae for predicting FFM will partition some of the change in TBW to FFM and some to Fat Mass. But if you weight is changing with some treatment that mainly affects Fat Mass then you might want to use baseline FFM and put the change in weight on the Fat Mass component.
The use of size for allometric scaling may also require some extra thinking about why the weight is changing. Volume of distribution may be sensitive to changes in weight due to fluid loss or accumulation but this probably won't affect clearance. On the other hand weight changes associated with growth in children seem to fit nicely with allometric theory because allometric size predicts the same clearance in children and adults (once maturation has been accounted for) (e.g. see Holford, Ma, Anderson 2012).
Best wishes,
Nick
1. Anderson BJ, Holford NHG. Mechanistic basis of using body size and maturation to predict clearance in humans. Drug Metab Pharmacokinet. 2009;24(1):25-36. 2. Holford NH, Ma SC, Anderson BJ. Prediction of morphine dose in humans. Paediatr Anaesth. 2012;22(3):209-22.
Quoted reply history
On 4/09/2013 11:20 a.m., Eleveld, DJ wrote:
> Hi Matt and Everyone,
>
> Whether or not "just using weight and CLCR should be enough" depends on whether
> you think that people who lost weight because of a drug (the formerly obese) are
> physilogically the same (with respect to the drugs in question) as those who were never
> obese. Are the formerly-obese maybe even a third group, different from non-obese and
> currently-obese?
>
> That said, making a distinction between healthy vs obese is odd. Obesity is a continuum and there
> shouldn't be model discontinuity when someone meets some arbitrary criteria. There shouldn't be
> choice "obese vs. non-obese", everything just comes as a smooth function of the
> covariates. Nature is "smooth" and, if possible, our models should be too.
>
> Warm regards,
>
> Douglas Eleveld
>
> -----Oorspronkelijk bericht-----
> Van: [email protected] [mailto:[email protected]] Namens
> Matt Hutmacher
> Verzonden: September 3, 2013 7:00 PM
> Aan: 'Nick Holford'; 'nmusers'
> Onderwerp: RE: [NMusers] Time-varing covariate and renal function as a covariate
>
> Hello Nick, Hans
>
> Thanks for the replies and sorry for being so vague. I wanted to get your opinions about
> such a scenario without providing information that might "steer" the dialogue.
>
> Perhaps a hypothetical will help clarify my scientific curiosity. Let's say at
> baseline we take measurements of weight (WT), etc. Assume Cockcroft-Gault is
> used to predict CLCR. We formulate a model either by Nick's or Hans' method
> below to relate WT and CLCR (a function of WT) to CL of the drug. However,
> over time, the drug changes WT... in some way the ratio of fat to lean mass is
> altered by the drug. Should we expect the same structural relationship to hold
> as we would have assumed at baseline (before we knew the drug changes WT)? And
> if so, then should we assume the same coefficients (exponents) for CLCR and WT
> would hold over time in such a model, such that just adjusting CLCR and WT as
> time varying covariates is all that is needed to be predictive? As another
> example, let's assume we do a pooled population PK using healthy volunteers and
> obese patients. Then, say a drug is administered that reduces WT. Should we
> use the same exponent
> (coefficient) for healthy volunteers and obese patients? And if the drug
> works, should at what point should we treat the obese patients as healthy
> volunteers - or would just using WT and CLCR take care of it?.
>
> Best regards,
> Matt
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]] On
> Behalf Of Nick Holford
> Sent: Monday, September 02, 2013 12:16
> To: 'nmusers'
> Subject: Re: [NMusers] Time-varing covariate and renal function as a covariate
>
> Matt,
>
> Thanks for your interest in this question. Hans and I have differing approaches
> for including 'renal function' but I think we agree on 'size'.
> Our differences of approach to 'renal function' are not very important for
> those who understand the biology and pharmacology. But its different when we
> have to talk to statisticians.
>
> While I recognize that you are not typical of statisticians (you know something
> about biology and pharmacology) it would help me (and probably
> Hans) if you stated more precisely what you mean by 'renal function' and 'size'
> and why you think there is a challenge if weight changes over time?
>
> Best wishes,
>
> Nick
>
> On 2/09/2013 9:04 a.m., J.H. Proost wrote:
>
> > Dear Matt,
> > I'm not quite sure that I fully understand your question. I would say
> > that a changing renal function and a changing weight over time can be
> > handled as described earlier by Nick Holford, or by the modified
> > approach I suggested. An important point is how to express renal
> > function.
> > Nick's method implies that 'size' should be excluded from 'renal
> > function', so CLCR needs to be normalized / standardized, e.g. using
> > CLCR in ml/min/1.73m2. Now, CLCR is a 'pure' measure of the kidney
> > function (of course, we know that its precision is rather poor, but
> > that is a different topic, interesting as well!). The factor
> > WEIGHT^0.75 deals with the factor 'size'. This approach treats CLCR as
> > a covariate similar to other covariates, making it more suitable for a
> > standardized approach for covariate analysis.
> > In the approach proposed by me, CLCR should be the 'individual's renal
> > clearance of creatinine', so it should expressed in ml/min (or
> > converted to e.g. l/h), and it should not be normalized /
> > standardized. Here, CLCR includes both kidney function and size (in
> > Nick's view a disadvantage, in my view an advantage), and the renal
> > part of the equation does not need further modification to take 'size'
> > into account. This approach treats CLCR as a 'special' covariate,
> > directly related to the renal clearance of the drug. This may be
> > advantageous for clinical purposes, e.g. dose calculation and
> > therapeutic drug monitoring.
> > In my view, both approaches have advantages and disadvantages.
> > 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: [email protected] <mailto:[email protected]>
>
> ________________________________
>
Dear Joe,
Thank you for your reply. You are right that one can model renal clearance using SeCr as you described. In fact, your approach is number three, after Nick's and mine (the order is purely arbitrary). It would be interesting to see real life examples and Monte Carlo simulations to see the performance of these approaches, which makes sense from a mechanistic / biological point of view.
Two minor remarks:
1) THETA(2) may be fixed to 1, since renal clearance will be inversely related to SeCr. Of course, THETA(2) may be estimated, but a value too far from 1 would be suspicious. 2) to keep the same format as for other covariates, I suggest to put SECR in the numerator
TVCL = THETA(1)*(SECR/STDCR)**THETA(2)
and using a negative value for THETA(2) (-1).
> How would you suggest smoothing is performed between Schwartz and C-G methods?
This can be achieved by the following procedure. The Cockcroft&Gault equation can be used for an age of 18 and older; the Schartz equation can be used for the age less than 20. Over the range 18-20 years, both equations can be used. The logical choice is to use the interpolated value, so:
CLcr(combined) = p * CLcr(C&G) + (1-p) * CLcr(Schwartz)
where p = (age - 18) / (20 - 18)
This guarantees a smooth relationship between age and CLcr, using both equations in their valid range. Even for equations that do not have an overlapping age range, such a range could be created by some minor extension of the ranges, e.g. by one year each; to cite Douglas: 'Nature is "smooth" and, if possible, our models should be too.'
Please note that a really smooth profile is obtained only if age is calculated from the current date and date of birth, using 'decimal' years.
DAYS360('date of birth','current date')/360
If you are interested, I can send you a simple spreadsheet.
best regards,
Hans
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: [email protected]
----- Original Message ----- From: "Standing Joseph (GREAT ORMOND STREET HOSPITAL FOR CHILDREN NHS FOUNDATION TRUST)" < [email protected] > To: "J.H.Proost" < [email protected] >; "Matt Hutmacher" < [email protected] >; "'Nick Holford'" < [email protected] >; "'nmusers'" < [email protected] >
Sent: Wednesday, September 04, 2013 3:17 PM
Subject: RE: [NMusers] Time-varing covariate and renal function as a covariate
Dear Hans,
If you are estimating GFR with C-G then you already have age (along with weight, sex and SeCr). Standardising SeCr is easy, for example:
TVCL = THETA(1)*(STDCR/SECR)**THETA(2)
where STDCR is the typical value of SeCr for that age (and/or sex in adults). You can find values for expected SeCr ranges for age usually reported alongside the measured level, from which you can take the mean or median as STDCR, or you could just use a published value. In adults STDCR differs between men and women, not so in children (the grey area of adolescence requires an extrapolation - see Johansson et al). If you are feeling particularly flashy you might want to use a published equation for predicting STDCR with age in children, like the Ceriotti 2008 model, that even goes down then up to account for maternal creatinine:
STDCR = -2.37330-12.91367*LOG(AGE)+23.93581*AGE**0.5 ; Mean SeCr, age adjusted (F. Ceriotti et al, Clinical Chemistry 54:3 559-566 (2008))
Another excellent paper where this method was used:
Hennig S et al, Clin Pharmacokinet. 2013;52(4):289-301.
How would you suggest smoothing is performed between Schwartz and C-G methods?
Best wishes,
Joe
Hans,
Thanks for pointing out the scientifically obvious that the empirical descriptive statisticians seem to be unaware of (your Minor Remark 1).
The same inability to think about the science can be found in this MDRD eGFR formula:
http://en.wikipedia.org/wiki/Renal_function
where the estimated exponent of -0.999 is proposed instead of the theoretically obvious value of -1.
Why is this theoretically obvious? Because clearance=rate elimination * conc^-1
So the correct exponent for serum creatinine is -1.
Best wishes,
Nick
Quoted reply history
On 6/09/2013 1:15 p.m., J.H. Proost wrote:
> Dear Joe,
>
> Thank you for your reply. You are right that one can model renal clearance using SeCr as you described. In fact, your approach is number three, after Nick's and mine (the order is purely arbitrary). It would be interesting to see real life examples and Monte Carlo simulations to see the performance of these approaches, which makes sense from a mechanistic / biological point of view.
>
> Two minor remarks:
>
> 1) THETA(2) may be fixed to 1, since renal clearance will be inversely related to SeCr. Of course, THETA(2) may be estimated, but a value too far from 1 would be suspicious. 2) to keep the same format as for other covariates, I suggest to put SECR in the numerator
>
> TVCL = THETA(1)*(SECR/STDCR)**THETA(2)
>
> and using a negative value for THETA(2) (-1).
>
> > How would you suggest smoothing is performed between Schwartz and C-G methods?
>
> This can be achieved by the following procedure. The Cockcroft&Gault equation can be used for an age of 18 and older; the Schartz equation can be used for the age less than 20. Over the range 18-20 years, both equations can be used. The logical choice is to use the interpolated value, so:
>
> CLcr(combined) = p * CLcr(C&G) + (1-p) * CLcr(Schwartz)
>
> where p = (age - 18) / (20 - 18)
>
> This guarantees a smooth relationship between age and CLcr, using both equations in their valid range. Even for equations that do not have an overlapping age range, such a range could be created by some minor extension of the ranges, e.g. by one year each; to cite Douglas: 'Nature is "smooth" and, if possible, our models should be too.'
>
> Please note that a really smooth profile is obtained only if age is calculated from the current date and date of birth, using 'decimal' years.
>
> DAYS360('date of birth','current date')/360
>
> If you are interested, I can send you a simple spreadsheet.
>
> best regards,
>
> Hans
>
> 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: [email protected]
>
> ----- Original Message ----- From: "Standing Joseph (GREAT ORMOND STREET HOSPITAL FOR CHILDREN NHS FOUNDATION TRUST)" < [email protected] > To: "J.H.Proost" < [email protected] >; "Matt Hutmacher" < [email protected] >; "'Nick Holford'" < [email protected] >; "'nmusers'" < [email protected] >
>
> Sent: Wednesday, September 04, 2013 3:17 PM
>
> Subject: RE: [NMusers] Time-varing covariate and renal function as a covariate
>
> Dear Hans,
>
> If you are estimating GFR with C-G then you already have age (along with weight, sex and SeCr). Standardising SeCr is easy, for example:
>
> TVCL = THETA(1)*(STDCR/SECR)**THETA(2)
>
> where STDCR is the typical value of SeCr for that age (and/or sex in adults). You can find values for expected SeCr ranges for age usually reported alongside the measured level, from which you can take the mean or median as STDCR, or you could just use a published value. In adults STDCR differs between men and women, not so in children (the grey area of adolescence requires an extrapolation - see Johansson et al). If you are feeling particularly flashy you might want to use a published equation for predicting STDCR with age in children, like the Ceriotti 2008 model, that even goes down then up to account for maternal creatinine:
>
> STDCR = -2.37330-12.91367*LOG(AGE)+23.93581*AGE**0.5 ; Mean SeCr, age adjusted (F. Ceriotti et al, Clinical Chemistry 54:3 559-566 (2008))
>
> Another excellent paper where this method was used:
>
> Hennig S et al, Clin Pharmacokinet. 2013;52(4):289-301.
>
> How would you suggest smoothing is performed between Schwartz and C-G methods?
>
> Best wishes,
>
> Joe
--
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
email: [email protected]
http://holford.fmhs.auckland.ac.nz/
Holford NHG. Disease progression and neuroscience. Journal of Pharmacokinetics
and Pharmacodynamics. 2013;40:369-76
http://link.springer.com/article/10.1007/s10928-013-9316-2
Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and
adults. J Pharm Sci. 2013:
http://onlinelibrary.wiley.com/doi/10.1002/jps.23574/abstract
Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. 2013;2:
http://www.nature.com/psp/journal/v2/n5/full/psp201318a.html
Holford NHG. Clinical pharmacology = disease progression + drug action. British
Journal of Clinical Pharmacology. 2013:
http://onlinelibrary.wiley.com/doi/10.1111/bcp.12170/abstract