I have an interesting question I'd like to get the group's collective opinion
on. I am fitting a pediatric and adult pk dataset. I have fixed weight a
priori to its allometric exponents in the model. When I test serum creatinine
and estimated creatinine clearance equation as covariates in the model (power
function), both are statistically significant. CrCL appears to be a better
predictor than serum Cr (LRT = 22.7 vs 16.7). I have an issue with using CrCL
as a predictor in the model since it's estimate is based on weight and weight
is already in the model. Also, there might be collinearity issues with CrCL
and weight in the same model, even though they are both significant. Does
anyone have a good argument for using CrCL in the model instead of serum Cr?
Thanks
Pete bonate
Peter L. Bonate, PhD, FCP
Genzyme Corporation
Senior Director
Clinical Pharmacology and Pharmacokinetics
4545 Horizon Hill Blvd
San Antonio, TX 78229 USA
[email protected]
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
alea jacta est - The die is cast.
Julius Caesar
CrcL or Cr in pediatric model
Peter, Jakob, Leonid,
A practical example of how to deal with collinearity of age and weight
over a wide range (premature neonates to young adults) using GFR has
been recently reported (Rhodin et al 2008).
One way to overcome the somewhat imagined concern about using weight for
Clcr and weight for overall clearance is to predict Clcr for a standard
weight person and compute renal function relative to a normal standard
weight person. Then you can apply weight to clearance and not worry
about using weight 'twice' (Mould et al. 2002; Matthews et al. 2004).
Jakob's concern about using the same random effect for both portions of
clearance with and additive non-renal plus non-renal clearance model is
quite reasonable. However, I think it might be quite difficult to
estimate separate ETAs for each component of clearance unless one has
more than one estimate of total clearance with a different renal
function in order to estimate the individual components of clearance.
As I am sure you know I dont think it is a good idea to try to estimate
allometric exponents unless you have lots of subjects with a very wide
weight range AND you can be pretty confident (or dont care) that you
have accounted for all other factors affecting clearance that are
correlated with weight (see Anderson & Holford 2008 for an example of
how hard it is to get precise estimates).
Nick
Rhodin, M. M., B. J. Anderson, et al. (2008). "Human renal function
maturation: a quantitative description using weight and postmenstrual
age." Pediatr Nephrol. Epub
Mould, D. R., N. H. Holford, et al. (2002). "Population pharmacokinetic
and adverse event analysis of topotecan in patients with solid tumors."
Clinical Pharmacology & Therapeutics. 71(5): 334-48.
Matthews, I., C. Kirkpatrick, et al. (2004). "Quantitative justification
for target concentration intervention - Parameter variability and
predictive performance using population pharmacokinetic models for
aminoglycosides." British Journal of Clinical Pharmacology 58(1): 8-19.
Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of
size and maturity in pharmacokinetics." Annu Rev Pharmacol Toxicol 48:
303-32.
Ribbing, Jakob wrote:
> Correction, I meant WT 50 and 75 in the example below:
> 75^0.75/(50^0.75)=1.36
>
Quoted reply history
> -----Original Message-----
> From: Ribbing, Jakob
> Sent: 13 January 2009 00:50
> To: nmusers
> Subject: RE: [NMusers] CrcL or Cr in pediatric model
>
> Leonid,
>
> I usually prefer multiplicative parameterisation as well, since it is
> easier to set boundaries (which is not necessary for power models, but
> for multiplicative-linear models). However, boundaries on the additive
> covariate models can still be set indirectly, using EXIT statements (not
> as neat as boundaries directly on the THETAS, I admit).
>
> In this case it may possibly be more mechanistic using the additive
> parameterisation: For example if the non-renal CL is mainly liver, the
> two blood flows run in parallel and the two elimination processes are
> independent (except there may be a correlation between liver function
> and renal function related to something other than size). A
> multiplicative parameterisation contains an assumed interaction which is
> fixed and in this case may not be appropriate. If the drug is mainly
> eliminated via filtration, why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates, except
> WT), be expected to differ by 36% in CL? This is what you get using a
> multiplicative parameterisation. The fixed interaction may also drive
> the selection of the functional form (e.g. a power model vs a linear
> model for CRCL on CL). I do not know anything about Peter's specific
> example so this is just theoretical.
>
> Regarding 3 below, is the suggestion to estimate independent allometric
> models on CL for each level of renal function?
>
> Thanks
>
> Jakob
>
> -----Original Message-----
> From: owner-nmusers
> On Behalf Of Leonid Gibiansky
> Sent: 12 January 2009 23:30
> To: Bonate, Peter
> Cc: nmusers
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Hi Peter,
>
> If allometric exponent is fixed, collinearity is not an issue from the
> mathematical point of view (convergence, CI on parameter estimates,
> etc.). However, in this case CRCL can end up being significant due to
> additional WT dependence (that could differ from allometric) rather than
>
> due to renal function influence (that is not good if you need to
> interpret it as the renal impairment influence on PK).
>
> Few points to consider:
> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get
> rid of WT - CRCL dependence. If you need to use it in pediatric
> population, normalization could be different but the idea to normalize
> CRCL by something that is "normal CRCL for a given WT" should be valid.
> 2. In the pediatric population used for the analysis, are there any
> reasons to suspect that kids have impaired renal function ? If not, I
> would hesitate to use CRCL as a covariate.
> 3. Often, categorical description of renal impairment allows to
> decrease or remove the WT-CRCL correlation
> 4. Expressions to compute CRCL in pediatric population (note that
> most of those are normalized by BSA, as suggested in (1)) can be found
> here:
> http://www.globalrph.com/specialpop.htm
> http://www.thedrugmonitor.com/clcreqs.html
> 5. Couple of recent papers:
> http://www.clinchem.org/cgi/content/full/49/6/1011
> http://www.ajhp.org/cgi/content/abstract/37/11/1514
>
> Thanks
> Leonid
>
> P.S. I do not think that this is a good idea to use additive dependence:
>
> TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> Bonate, Peter wrote:
>
>> I have an interesting question I'd like to get the group's collective
>> opinion on. I am fitting a pediatric and adult pk dataset. I have
>> fixed weight a priori to its allometric exponents in the model. When
>>
> I
>
>> test serum creatinine and estimated creatinine clearance equation as
>> covariates in the model (power function), both are statistically
>> significant. CrCL appears to be a better predictor than serum Cr (LRT
>>
> =
>
>> 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the
>> model since it's estimate is based on weight and weight is already in
>> the model. Also, there might be collinearity issues with CrCL and
>> weight in the same model, even though they are both significant. Does
>>
>
>
>> anyone have a good argument for using CrCL in the model instead of
>>
> serum Cr?
>
>> Thanks
>>
>> Pete bonate
>>
>>
>>
>> Peter L. Bonate, PhD, FCP
>> Genzyme Corporation
>> Senior Director
>> Clinical Pharmacology and Pharmacokinetics
>> 4545 Horizon Hill Blvd
>> San Antonio, TX 78229 USA
>> _peter.bonate
>> phone: 210-949-8662
>> fax: 210-949-8219
>> crackberry: 210-315-2713
>>
>> alea jacta est - The die is cast.
>>
>> Julius Caesar
>>
>>
>>
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holford
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Pete,
Is the drug cleared almost completely thru renal elimination?
Otherwise, maybe a slope intercept model for CL as a function of CRCL?
TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
The intercept is nonrenal CL according to the allometric model and the
slope according to CRCL. This model may be inappropriate if renally
impared are included in the dataset or if there are other reasons to why
the linear model for CRCL may be inappropriate. With this model the
collinearity is a smaller problem since the exponent in the allometric
model is not estimated.
Best regards
Jakob
Quoted reply history
________________________________
From: [email protected] [mailto:[email protected]]
On Behalf Of Bonate, Peter
Sent: 12 January 2009 21:52
To: [email protected]
Subject: [NMusers] CrcL or Cr in pediatric model
I have an interesting question I'd like to get the group's collective
opinion on. I am fitting a pediatric and adult pk dataset. I have
fixed weight a priori to its allometric exponents in the model. When I
test serum creatinine and estimated creatinine clearance equation as
covariates in the model (power function), both are statistically
significant. CrCL appears to be a better predictor than serum Cr (LRT =
22.7 vs 16.7). I have an issue with using CrCL as a predictor in the
model since it's estimate is based on weight and weight is already in
the model. Also, there might be collinearity issues with CrCL and
weight in the same model, even though they are both significant. Does
anyone have a good argument for using CrCL in the model instead of serum
Cr?
Thanks
Pete bonate
Peter L. Bonate, PhD, FCP
Genzyme Corporation
Senior Director
Clinical Pharmacology and Pharmacokinetics
4545 Horizon Hill Blvd
San Antonio, TX 78229 USA
[email protected] <mailto:[email protected]>
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
alea jacta est - The die is cast.
Julius Caesar
Hi Peter,
If allometric exponent is fixed, collinearity is not an issue from the mathematical point of view (convergence, CI on parameter estimates, etc.). However, in this case CRCL can end up being significant due to additional WT dependence (that could differ from allometric) rather than due to renal function influence (that is not good if you need to interpret it as the renal impairment influence on PK).
Few points to consider:
1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get rid of WT - CRCL dependence. If you need to use it in pediatric population, normalization could be different but the idea to normalize CRCL by something that is "normal CRCL for a given WT" should be valid. 2. In the pediatric population used for the analysis, are there any reasons to suspect that kids have impaired renal function ? If not, I would hesitate to use CRCL as a covariate. 3. Often, categorical description of renal impairment allows to decrease or remove the WT-CRCL correlation 4. Expressions to compute CRCL in pediatric population (note that most of those are normalized by BSA, as suggested in (1)) can be found here:
http://www.globalrph.com/specialpop.htm
http://www.thedrugmonitor.com/clcreqs.html
5. Couple of recent papers:
http://www.clinchem.org/cgi/content/full/49/6/1011
http://www.ajhp.org/cgi/content/abstract/37/11/1514
Thanks
Leonid
P.S. I do not think that this is a good idea to use additive dependence:
TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Bonate, Peter wrote:
> I have an interesting question I'd like to get the group's collective opinion on. I am fitting a pediatric and adult pk dataset. I have fixed weight a priori to its allometric exponents in the model. When I test serum creatinine and estimated creatinine clearance equation as covariates in the model (power function), both are statistically significant. CrCL appears to be a better predictor than serum Cr (LRT = 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the model since it's estimate is based on weight and weight is already in the model. Also, there might be collinearity issues with CrCL and weight in the same model, even though they are both significant. Does anyone have a good argument for using CrCL in the model instead of serum Cr?
>
> Thanks
>
> Pete bonate
>
> Peter L. Bonate, PhD, FCP
> Genzyme Corporation
> Senior Director
> Clinical Pharmacology and Pharmacokinetics
> 4545 Horizon Hill Blvd
> San Antonio, TX 78229 USA
> [email protected]_ <mailto:[email protected]>
> phone: 210-949-8662
> fax: 210-949-8219
> crackberry: 210-315-2713
>
> alea jacta est - The die is cast.
>
> Julius Caesar
Leonid,
I usually prefer multiplicative parameterisation as well, since it is
easier to set boundaries (which is not necessary for power models, but
for multiplicative-linear models). However, boundaries on the additive
covariate models can still be set indirectly, using EXIT statements (not
as neat as boundaries directly on the THETAS, I admit).
In this case it may possibly be more mechanistic using the additive
parameterisation: For example if the non-renal CL is mainly liver, the
two blood flows run in parallel and the two elimination processes are
independent (except there may be a correlation between liver function
and renal function related to something other than size). A
multiplicative parameterisation contains an assumed interaction which is
fixed and in this case may not be appropriate. If the drug is mainly
eliminated via filtration, why would two persons, with WT 50 and 70 kg
but otherwise identical (including CRCL and any other covariates, except
WT), be expected to differ by 36% in CL? This is what you get using a
multiplicative parameterisation. The fixed interaction may also drive
the selection of the functional form (e.g. a power model vs a linear
model for CRCL on CL). I do not know anything about Peter's specific
example so this is just theoretical.
Regarding 3 below, is the suggestion to estimate independent allometric
models on CL for each level of renal function?
Thanks
Jakob
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On Behalf Of Leonid Gibiansky
Sent: 12 January 2009 23:30
To: Bonate, Peter
Cc: [email protected]
Subject: Re: [NMusers] CrcL or Cr in pediatric model
Hi Peter,
If allometric exponent is fixed, collinearity is not an issue from the
mathematical point of view (convergence, CI on parameter estimates,
etc.). However, in this case CRCL can end up being significant due to
additional WT dependence (that could differ from allometric) rather than
due to renal function influence (that is not good if you need to
interpret it as the renal impairment influence on PK).
Few points to consider:
1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get
rid of WT - CRCL dependence. If you need to use it in pediatric
population, normalization could be different but the idea to normalize
CRCL by something that is "normal CRCL for a given WT" should be valid.
2. In the pediatric population used for the analysis, are there any
reasons to suspect that kids have impaired renal function ? If not, I
would hesitate to use CRCL as a covariate.
3. Often, categorical description of renal impairment allows to
decrease or remove the WT-CRCL correlation
4. Expressions to compute CRCL in pediatric population (note that
most of those are normalized by BSA, as suggested in (1)) can be found
here:
http://www.globalrph.com/specialpop.htm
http://www.thedrugmonitor.com/clcreqs.html
5. Couple of recent papers:
http://www.clinchem.org/cgi/content/full/49/6/1011
http://www.ajhp.org/cgi/content/abstract/37/11/1514
Thanks
Leonid
P.S. I do not think that this is a good idea to use additive dependence:
TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Bonate, Peter wrote:
> I have an interesting question I'd like to get the group's collective
> opinion on. I am fitting a pediatric and adult pk dataset. I have
> fixed weight a priori to its allometric exponents in the model. When
I
> test serum creatinine and estimated creatinine clearance equation as
> covariates in the model (power function), both are statistically
> significant. CrCL appears to be a better predictor than serum Cr (LRT
=
> 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the
> model since it's estimate is based on weight and weight is already in
> the model. Also, there might be collinearity issues with CrCL and
> weight in the same model, even though they are both significant. Does
> anyone have a good argument for using CrCL in the model instead of
serum Cr?
>
> Thanks
>
> Pete bonate
>
>
>
> Peter L. Bonate, PhD, FCP
> Genzyme Corporation
> Senior Director
> Clinical Pharmacology and Pharmacokinetics
> 4545 Horizon Hill Blvd
> San Antonio, TX 78229 USA
> [email protected]_ <mailto:[email protected]>
> phone: 210-949-8662
> fax: 210-949-8219
> crackberry: 210-315-2713
>
> alea jacta est - The die is cast.
>
> Julius Caesar
>
>
Peter, Jakob, Leonid,
A practical example of how to deal with collinearity of age and weight over a wide range (premature neonates to young adults) using GFR has been recently reported (Rhodin et al 2008).
One way to overcome the somewhat imagined concern about using weight for Clcr and weight for overall clearance is to predict Clcr for a standard weight person and compute renal function relative to a normal standard weight person. Then you can apply weight to clearance and not worry about using weight 'twice' (Mould et al. 2002; Matthews et al. 2004).
Jakob's concern about using the same random effect for both portions of clearance with and additive non-renal plus non-renal clearance model is quite reasonable. However, I think it might be quite difficult to estimate separate ETAs for each component of clearance unless one has more than one estimate of total clearance with a different renal function in order to estimate the individual components of clearance.
As I am sure you know I dont think it is a good idea to try to estimate allometric exponents unless you have lots of subjects with a very wide weight range AND you can be pretty confident (or dont care) that you have accounted for all other factors affecting clearance that are correlated with weight (see Anderson & Holford 2008 for an example of how hard it is to get precise estimates).
Nick
Rhodin, M. M., B. J. Anderson, et al. (2008). "Human renal function maturation: a quantitative description using weight and postmenstrual age." Pediatr Nephrol. Epub Mould, D. R., N. H. Holford, et al. (2002). "Population pharmacokinetic and adverse event analysis of topotecan in patients with solid tumors." Clinical Pharmacology & Therapeutics. 71(5): 334-48. Matthews, I., C. Kirkpatrick, et al. (2004). "Quantitative justification for target concentration intervention - Parameter variability and predictive performance using population pharmacokinetic models for aminoglycosides." British Journal of Clinical Pharmacology 58(1): 8-19. Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of size and maturity in pharmacokinetics." Annu Rev Pharmacol Toxicol 48: 303-32.
Ribbing, Jakob wrote:
> Correction, I meant WT 50 and 75 in the example below:
> 75^0.75/(50^0.75)=1.36
>
Quoted reply history
> -----Original Message-----
>
> From: Ribbing, Jakob Sent: 13 January 2009 00:50
>
> To: [email protected]; 'Leonid Gibiansky'; Bonate, Peter
> Subject: RE: [NMusers] CrcL or Cr in pediatric model
>
> Leonid,
>
> I usually prefer multiplicative parameterisation as well, since it is
> easier to set boundaries (which is not necessary for power models, but
> for multiplicative-linear models). However, boundaries on the additive
> covariate models can still be set indirectly, using EXIT statements (not
> as neat as boundaries directly on the THETAS, I admit).
>
> In this case it may possibly be more mechanistic using the additive
> parameterisation: For example if the non-renal CL is mainly liver, the
> two blood flows run in parallel and the two elimination processes are
> independent (except there may be a correlation between liver function
> and renal function related to something other than size). A
> multiplicative parameterisation contains an assumed interaction which is
> fixed and in this case may not be appropriate. If the drug is mainly
> eliminated via filtration, why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates, except
> WT), be expected to differ by 36% in CL? This is what you get using a
> multiplicative parameterisation. The fixed interaction may also drive
> the selection of the functional form (e.g. a power model vs a linear
> model for CRCL on CL). I do not know anything about Peter's specific
> example so this is just theoretical.
>
> Regarding 3 below, is the suggestion to estimate independent allometric
> models on CL for each level of renal function?
>
> Thanks
>
> Jakob
>
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> On Behalf Of Leonid Gibiansky
> Sent: 12 January 2009 23:30
> To: Bonate, Peter
> Cc: [email protected]
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Hi Peter,
>
> If allometric exponent is fixed, collinearity is not an issue from the mathematical point of view (convergence, CI on parameter estimates, etc.). However, in this case CRCL can end up being significant due to additional WT dependence (that could differ from allometric) rather than
>
> due to renal function influence (that is not good if you need to interpret it as the renal impairment influence on PK).
>
> Few points to consider:
>
> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get rid of WT - CRCL dependence. If you need to use it in pediatric population, normalization could be different but the idea to normalize CRCL by something that is "normal CRCL for a given WT" should be valid. 2. In the pediatric population used for the analysis, are there any reasons to suspect that kids have impaired renal function ? If not, I would hesitate to use CRCL as a covariate. 3. Often, categorical description of renal impairment allows to decrease or remove the WT-CRCL correlation 4. Expressions to compute CRCL in pediatric population (note that most of those are normalized by BSA, as suggested in (1)) can be found
>
> here:
> http://www.globalrph.com/specialpop.htm
> http://www.thedrugmonitor.com/clcreqs.html
> 5. Couple of recent papers:
> http://www.clinchem.org/cgi/content/full/49/6/1011
> http://www.ajhp.org/cgi/content/abstract/37/11/1514
>
> Thanks
> Leonid
>
> P.S. I do not think that this is a good idea to use additive dependence:
>
> TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
> Bonate, Peter wrote:
>
> > I have an interesting question I'd like to get the group's collective opinion on. I am fitting a pediatric and adult pk dataset. I have fixed weight a priori to its allometric exponents in the model. When
>
> I
>
> > test serum creatinine and estimated creatinine clearance equation as covariates in the model (power function), both are statistically significant. CrCL appears to be a better predictor than serum Cr (LRT
>
> =
>
> > 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the model since it's estimate is based on weight and weight is already in the model. Also, there might be collinearity issues with CrCL and weight in the same model, even though they are both significant. Does
>
> > anyone have a good argument for using CrCL in the model instead of
>
> serum Cr?
>
> > Thanks
> >
> > Pete bonate
> >
> > Peter L. Bonate, PhD, FCP
> > Genzyme Corporation
> > Senior Director
> > Clinical Pharmacology and Pharmacokinetics
> > 4545 Horizon Hill Blvd
> > San Antonio, TX 78229 USA
> > [email protected]_ <mailto:[email protected]>
> > phone: 210-949-8662
> > fax: 210-949-8219
> > crackberry: 210-315-2713
> >
> > alea jacta est - The die is cast.
> >
> > Julius Caesar
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Jakob,
I'm not sure that I would have confidence in the findings of
"fixed-effect) interaction component between WT and CRCL (with the hope
of concluding it is not needed)" approach. I know we tend to think in
this type of sequential manner with respect to covariate relationship
testing but, as Nick has pointed out previously, the ability to test
such relationships depends quite a bit on the sample population. More
problematic is the limitations of CRCL as a marker of developmental
changes in renal function and the ability of a "fixed effect" to capture
subtle changes across a potentially narrow WT range. I'm more in favor
of simulation approaches to verify (or not) relationships that are
consistent with the observed data and of course physiologically
plausible based on the pharmacokinetic attributes of the compound in
question.
Cheers.
Jeff
Jeffrey S. Barrett, Ph.D., FCP
Research Associate Professor, Pediatrics
Director, Pediatric Pharmacology Research Unit,
Laboratory for Applied PK/PD
Clinical Pharmacology & Therapeutics
Abramson Research Center, Rm 916H
The Children's Hospital of Philadelphia
3615 Civic Center Blvd.
Philadelphia, PA 19104
KMAS (Kinetic Modeling & Simulation)
Institute for Translational Medicine
University of Pennsylvania
email: [email protected]
Ph: (267) 426-5479
>>> "Ribbing, Jakob" <[email protected]> 01/13/09 2:31 AM >>>
Thank you for this, Nick.
Regarding estimating separate eta for the two CL components I completely
agree with you. When I talked about a possible correlation component
between renal and non-renal CL that could not be attributed to size, my
intention was not to estimate separate random components for the two
processes. What would be possible, however, were to estimate a
(fixed-effect) interaction component between WT and CRCL (with the hope
of concluding it is not needed). This test can thus provide some further
support to that other important covariates have been integrated
correctly, or point to a potential problem.
Jakob
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On Behalf Of Nick Holford
Sent: 13 January 2009 01:44
To: nmusers
Subject: Re: [NMusers] CrcL or Cr in pediatric model
Peter, Jakob, Leonid,
A practical example of how to deal with collinearity of age and weight
over a wide range (premature neonates to young adults) using GFR has
been recently reported (Rhodin et al 2008).
One way to overcome the somewhat imagined concern about using weight for
Clcr and weight for overall clearance is to predict Clcr for a standard
weight person and compute renal function relative to a normal standard
weight person. Then you can apply weight to clearance and not worry
about using weight 'twice' (Mould et al. 2002; Matthews et al. 2004).
Jakob's concern about using the same random effect for both portions of
clearance with and additive non-renal plus non-renal clearance model is
quite reasonable. However, I think it might be quite difficult to
estimate separate ETAs for each component of clearance unless one has
more than one estimate of total clearance with a different renal
function in order to estimate the individual components of clearance.
As I am sure you know I dont think it is a good idea to try to estimate
allometric exponents unless you have lots of subjects with a very wide
weight range AND you can be pretty confident (or dont care) that you
have accounted for all other factors affecting clearance that are
correlated with weight (see Anderson & Holford 2008 for an example of
how hard it is to get precise estimates).
Nick
Rhodin, M. M., B. J. Anderson, et al. (2008). "Human renal function
maturation: a quantitative description using weight and postmenstrual
age." Pediatr Nephrol. Epub
Mould, D. R., N. H. Holford, et al. (2002). "Population pharmacokinetic
and adverse event analysis of topotecan in patients with solid tumors."
Clinical Pharmacology & Therapeutics. 71(5): 334-48.
Matthews, I., C. Kirkpatrick, et al. (2004). "Quantitative justification
for target concentration intervention - Parameter variability and
predictive performance using population pharmacokinetic models for
aminoglycosides." British Journal of Clinical Pharmacology 58(1): 8-19.
Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of
size and maturity in pharmacokinetics." Annu Rev Pharmacol Toxicol 48:
303-32.
Ribbing, Jakob wrote:
> Correction, I meant WT 50 and 75 in the example below:
> 75^0.75/(50^0.75)=1.36
>
> -----Original Message-----
> From: Ribbing, Jakob
> Sent: 13 January 2009 00:50
> To: [email protected]; 'Leonid Gibiansky'; Bonate, Peter
> Subject: RE: [NMusers] CrcL or Cr in pediatric model
>
> Leonid,
>
> I usually prefer multiplicative parameterisation as well, since it is
> easier to set boundaries (which is not necessary for power models, but
> for multiplicative-linear models). However, boundaries on the additive
> covariate models can still be set indirectly, using EXIT statements
(not
> as neat as boundaries directly on the THETAS, I admit).
>
> In this case it may possibly be more mechanistic using the additive
> parameterisation: For example if the non-renal CL is mainly liver, the
> two blood flows run in parallel and the two elimination processes are
> independent (except there may be a correlation between liver function
> and renal function related to something other than size). A
> multiplicative parameterisation contains an assumed interaction which
is
> fixed and in this case may not be appropriate. If the drug is mainly
> eliminated via filtration, why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates,
except
> WT), be expected to differ by 36% in CL? This is what you get using a
> multiplicative parameterisation. The fixed interaction may also drive
> the selection of the functional form (e.g. a power model vs a linear
> model for CRCL on CL). I do not know anything about Peter's specific
> example so this is just theoretical.
>
> Regarding 3 below, is the suggestion to estimate independent
allometric
> models on CL for each level of renal function?
>
> Thanks
>
> Jakob
>
> -----Original Message-----
> From: [email protected]
[mailto:[email protected]]
> On Behalf Of Leonid Gibiansky
> Sent: 12 January 2009 23:30
> To: Bonate, Peter
> Cc: [email protected]
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Hi Peter,
>
> If allometric exponent is fixed, collinearity is not an issue from the
> mathematical point of view (convergence, CI on parameter estimates,
> etc.). However, in this case CRCL can end up being significant due to
> additional WT dependence (that could differ from allometric) rather
than
>
> due to renal function influence (that is not good if you need to
> interpret it as the renal impairment influence on PK).
>
> Few points to consider:
> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get
> rid of WT - CRCL dependence. If you need to use it in pediatric
> population, normalization could be different but the idea to normalize
> CRCL by something that is "normal CRCL for a given WT" should be
valid.
> 2. In the pediatric population used for the analysis, are there any
> reasons to suspect that kids have impaired renal function ? If not, I
> would hesitate to use CRCL as a covariate.
> 3. Often, categorical description of renal impairment allows to
> decrease or remove the WT-CRCL correlation
> 4. Expressions to compute CRCL in pediatric population (note that
> most of those are normalized by BSA, as suggested in (1)) can be found
> here:
> http://www.globalrph.com/specialpop.htm
> http://www.thedrugmonitor.com/clcreqs.html
> 5. Couple of recent papers:
> http://www.clinchem.org/cgi/content/full/49/6/1011
> http://www.ajhp.org/cgi/content/abstract/37/11/1514
>
> Thanks
> Leonid
>
> P.S. I do not think that this is a good idea to use additive
dependence:
>
> TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> Bonate, Peter wrote:
>
>> I have an interesting question I'd like to get the group's collective
>> opinion on. I am fitting a pediatric and adult pk dataset. I have
>> fixed weight a priori to its allometric exponents in the model. When
>>
> I
>
>> test serum creatinine and estimated creatinine clearance equation as
>> covariates in the model (power function), both are statistically
>> significant. CrCL appears to be a better predictor than serum Cr
(LRT
>>
> =
>
>> 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the
>> model since it's estimate is based on weight and weight is already in
>> the model. Also, there might be collinearity issues with CrCL and
>> weight in the same model, even though they are both significant.
Does
>>
>
>
>> anyone have a good argument for using CrCL in the model instead of
>>
> serum Cr?
>
>> Thanks
>>
>> Pete bonate
>>
>>
>>
>> Peter L. Bonate, PhD, FCP
>> Genzyme Corporation
>> Senior Director
>> Clinical Pharmacology and Pharmacokinetics
>> 4545 Horizon Hill Blvd
>> San Antonio, TX 78229 USA
>> [email protected]_ <mailto:[email protected]>
>> phone: 210-949-8662
>> fax: 210-949-8219
>> crackberry: 210-315-2713
>>
>> alea jacta est - The die is cast.
>>
>> Julius Caesar
>>
>>
>>
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Jakob,
Restrictions on the parameter values is not the only (and not the major) problem with additive parametrization. In this specific case, CRCL (as clearance) increases proportionally to WT^(3/4) (or similar power, if you accept that allometric scaling has biological meaning or that the filtration rate is proportional to the kidney size). Then you have
TVCL=THETA(1)*WT^(3/4)+THETA(2)*WT^(3/4)
(where the second term approximates CRCL dependence on WT).
Clearly, the model is unstable.
Answering the question:
> why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates,
> except WT), be expected to differ by 36% in CL?
we are back to the problem of correlation. If two persons of different WT have the same CRCL, they should differ by the "health" of their renal function. I would rater have the model
CL=THETA(1)*(WT/70)^(3/4)*(CRCL/BSA)^GAMMA
Then, if two subjects (50 and 70 kg) have the same CRCL, their CL will be influenced by WT, and by renal function (in this particular realization, CRCL per body surface area). While the result could be the same as in
CL ~ CRCL,
we described two separate and important dependencies:
CL ~ WT; and CL ~ renal function
For the patient that you mentioned, they act in the opposite directions and cancel each other, but it is important to describe both dependencies.
> Regarding 3 below, is the suggestion to estimate
> independent allometric
> models on CL for each level of renal function?
The suggestion was to define the renal disease as categorical variable, and then correct CL, for example:
TCL ~ THETA(1) (for healthy)
TCL ~ THETA(2) (for patients with severe renal impairment)
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Ribbing, Jakob wrote:
> Leonid,
>
> I usually prefer multiplicative parameterisation as well, since it is
> easier to set boundaries (which is not necessary for power models, but
> for multiplicative-linear models). However, boundaries on the additive
> covariate models can still be set indirectly, using EXIT statements (not
> as neat as boundaries directly on the THETAS, I admit).
>
> In this case it may possibly be more mechanistic using the additive
> parameterisation: For example if the non-renal CL is mainly liver, the
> two blood flows run in parallel and the two elimination processes are
> independent (except there may be a correlation between liver function
> and renal function related to something other than size). A
> multiplicative parameterisation contains an assumed interaction which is
> fixed and in this case may not be appropriate. If the drug is mainly
> eliminated via filtration, why would two persons, with WT 50 and 70 kg
> but otherwise identical (including CRCL and any other covariates, except
> WT), be expected to differ by 36% in CL? This is what you get using a
> multiplicative parameterisation. The fixed interaction may also drive
> the selection of the functional form (e.g. a power model vs a linear
> model for CRCL on CL). I do not know anything about Peter's specific
> example so this is just theoretical.
>
> Regarding 3 below, is the suggestion to estimate independent allometric
> models on CL for each level of renal function?
>
> Thanks
>
> Jakob
>
Quoted reply history
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> On Behalf Of Leonid Gibiansky
> Sent: 12 January 2009 23:30
> To: Bonate, Peter
> Cc: [email protected]
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Hi Peter,
>
> If allometric exponent is fixed, collinearity is not an issue from the mathematical point of view (convergence, CI on parameter estimates, etc.). However, in this case CRCL can end up being significant due to additional WT dependence (that could differ from allometric) rather than
>
> due to renal function influence (that is not good if you need to interpret it as the renal impairment influence on PK).
>
> Few points to consider:
>
> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to get rid of WT - CRCL dependence. If you need to use it in pediatric population, normalization could be different but the idea to normalize CRCL by something that is "normal CRCL for a given WT" should be valid. 2. In the pediatric population used for the analysis, are there any reasons to suspect that kids have impaired renal function ? If not, I would hesitate to use CRCL as a covariate. 3. Often, categorical description of renal impairment allows to decrease or remove the WT-CRCL correlation 4. Expressions to compute CRCL in pediatric population (note that most of those are normalized by BSA, as suggested in (1)) can be found
>
> here:
> http://www.globalrph.com/specialpop.htm
> http://www.thedrugmonitor.com/clcreqs.html
> 5. Couple of recent papers:
> http://www.clinchem.org/cgi/content/full/49/6/1011
> http://www.ajhp.org/cgi/content/abstract/37/11/1514
>
> Thanks
> Leonid
>
> P.S. I do not think that this is a good idea to use additive dependence:
>
> TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
> Bonate, Peter wrote:
>
> > I have an interesting question I'd like to get the group's collective opinion on. I am fitting a pediatric and adult pk dataset. I have fixed weight a priori to its allometric exponents in the model. When
>
> I
>
> > test serum creatinine and estimated creatinine clearance equation as covariates in the model (power function), both are statistically significant. CrCL appears to be a better predictor than serum Cr (LRT
>
> =
>
> > 22.7 vs 16.7). I have an issue with using CrCL as a predictor in the model since it's estimate is based on weight and weight is already in the model. Also, there might be collinearity issues with CrCL and weight in the same model, even though they are both significant. Does
>
> > anyone have a good argument for using CrCL in the model instead of
>
> serum Cr?
>
> > Thanks
> >
> > Pete bonate
> >
> > Peter L. Bonate, PhD, FCP
> > Genzyme Corporation
> > Senior Director
> > Clinical Pharmacology and Pharmacokinetics
> > 4545 Horizon Hill Blvd
> > San Antonio, TX 78229 USA
> > [email protected]_ <mailto:[email protected]>
> > phone: 210-949-8662
> > fax: 210-949-8219
> > crackberry: 210-315-2713
> >
> > alea jacta est - The die is cast.
> >
> > Julius Caesar
Leonid,
As I understand the linear model you suggested it can be simplified* to
this structure:
THETA(1)*((WT/70)^(3/4)+THETA(2)*CRCL)
I call this additive, because the two covariates affect TVCL in an
absolute sense, without interaction. My main message was that I find
this model appealing, because it has the properties:
a)There is a linear increase of CL with CRCL
b)An increase in CRCL increases CL with an absolute number which is the
same for two subjects with different WT
The same can not be said about this model:
TVCL=THETA(1)*(WT/70)^(3/4) * RF^GAMMA
The latter model carries a built-in interaction which may provide a
better description of the data in situations where e.g. non-renal
elimination decreases with CRCL or where the secretory component of
renal elimination is more important for creatinine than for the drug.
However, in the opposite situations the interaction would be working in
the wrong direction (assuming GAMMA<1). Maybe we can leave what
basic-model assumption we want to use as a matter of personal or
drug-specific preference?
Best
Jakob
PS
Nonmem users is like an octopus: Just when you think you are free one of
its threads pulls you back in again :>)
Much of this discussion is around additivity. If I have understood the
definition of additivity wrong, then I apologies on beforehand, so that
this can still be my final "contribution" to this thread. Likewise if I
misunderstood what model Leonid was actually suggesting...
DS
*This is how I have simplified the suggested linear model:
TVCL=THETA(1)*(WT/70)^(3/4) * (1+THETA(2)*RF)=
=THETA(1)*(WT/70)^(3/4) * (1+THETA(2)*CRCL/(WT/70)^(3/4)) =
=THETA(1)*(WT/70)^(3/4)+THETA(1)*(WT/70)^(3/4)*THETA(2)*CRCL/(WT/70)^(3/
4)=
=THETA(1)*((WT/70)^(3/4)+THETA(2)*CRCL)
Or =THETA(1)* (WT/70)^(3/4)+THETA(1)*THETA(2)*CRCL
Similar: THETA(1)* (WT/70)^(3/4)+THETA(2)*CRCL (where the interpretation
of THETA(2) changed from the line before)
Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]
On Behalf Of Leonid Gibiansky
Sent: 13 January 2009 22:50
To: [email protected]
Subject: Re: [NMusers] CrcL or Cr in pediatric model
Jakob,
The model that I mentioned is not additive; it is multiplicative:
Parameter= MeanValue*Effect1(WT)*Effect2(RF)
but the effect of RF is expressed as a linear function of RF
Effect2(RF) = 1 + THETA()*RF
Leonid
Hi Jakob,
I am sorry, I made an error in that model, it should be
CL=THETA(1)*(WT/70)^(3/4) * [1+THETA(2)*(RF-RF0)]
For subjects with the normal RF (RF=RF0) the second term is one. As always, all covariate expressions should be centered at "normal" values.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Ribbing, Jakob wrote:
> Leonid,
>
> As I understand the linear model you suggested it can be simplified* to
> this structure:
> THETA(1)*((WT/70)^(3/4)+THETA(2)*CRCL)
>
> I call this additive, because the two covariates affect TVCL in an
> absolute sense, without interaction. My main message was that I find
> this model appealing, because it has the properties:
> a)There is a linear increase of CL with CRCL
> b)An increase in CRCL increases CL with an absolute number which is the
> same for two subjects with different WT
>
> The same can not be said about this model:
> TVCL=THETA(1)*(WT/70)^(3/4) * RF^GAMMA
> The latter model carries a built-in interaction which may provide a
> better description of the data in situations where e.g. non-renal
> elimination decreases with CRCL or where the secretory component of
> renal elimination is more important for creatinine than for the drug.
> However, in the opposite situations the interaction would be working in
> the wrong direction (assuming GAMMA<1). Maybe we can leave what
> basic-model assumption we want to use as a matter of personal or
> drug-specific preference?
>
> Best
>
> Jakob
>
> PS
> Nonmem users is like an octopus: Just when you think you are free one of
> its threads pulls you back in again :>)
> Much of this discussion is around additivity. If I have understood the
> definition of additivity wrong, then I apologies on beforehand, so that
> this can still be my final "contribution" to this thread. Likewise if I
> misunderstood what model Leonid was actually suggesting...
> DS
>
> *This is how I have simplified the suggested linear model:
> TVCL=THETA(1)*(WT/70)^(3/4) * (1+THETA(2)*RF)=
> =THETA(1)*(WT/70)^(3/4) * (1+THETA(2)*CRCL/(WT/70)^(3/4)) =
> =THETA(1)*(WT/70)^(3/4)+THETA(1)*(WT/70)^(3/4)*THETA(2)*CRCL/(WT/70)^(3/
> 4)=
> =THETA(1)*((WT/70)^(3/4)+THETA(2)*CRCL)
>
> Or =THETA(1)* (WT/70)^(3/4)+THETA(1)*THETA(2)*CRCL
> Similar: THETA(1)* (WT/70)^(3/4)+THETA(2)*CRCL (where the interpretation
> of THETA(2) changed from the line before)
>
Quoted reply history
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> On Behalf Of Leonid Gibiansky
> Sent: 13 January 2009 22:50
> To: [email protected]
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Jakob,
>
> The model that I mentioned is not additive; it is multiplicative:
>
> Parameter= MeanValue*Effect1(WT)*Effect2(RF)
>
> but the effect of RF is expressed as a linear function of RF
> Effect2(RF) = 1 + THETA()*RF
>
> Leonid