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From: Nick Holford <n.holford_at_auckland.ac.nz>

Date: Wed, 1 Jun 2016 10:27:04 +0200

Dear Steve,

Thanks for your responses of 22 May and 24 May PDT. Due to some

unexplained technical problem I have not been receiving posts from

PharmPK since 23 May and only just became aware of your 24 May post. I

have tried twice to post a response to PharmPK but it has not appeared

on the list as far as I can tell. I am therefore transferring this

discussion to nmusers.

On 22 May you wrote “I am not aware of any theory that supports scaling

by weight to the 3/4 power WITHIN A SPECIES”. Having read the 22 May

post from Douglas Eleveld and my own reply do you now accept that the

theory of West et al. supports 3/4 power weight scaling within a species

including humans?

My comments below are in response to your PharmPK post of 24 May.

Best wishes,

Nick

SS:

Dear Nick:

You stated in your comments to me, both on NMUSERS and on PHARMPK, that

a paper of yours with Dr. McCune offered a validation of the use of

allometric scaling. Dennis Fisher has already commented on this paper.

Dennis said I might have additional comments. As usual, Dennis is right.

The paper is McCune et al, Busulfan in infant to adult hematopoietic

cell transplant recipients: a population pharmacokinetic model for

initial and Bayesian dose personalization.. Clin Cancer Res.

2014;20:754-63. Based on my reading of your paper, and the supplementary

material, I would like to offer several observations.

1. Quoting from page 755: “To characterize busulfan pharmacokinetics

over the entire age continuum, all clearance (CL,Q) and volume (V1, V2)

parameters were scaled for body size and composition using allometric

theory and predicted fat-free mass.” In other words, you assumed

allometric theory at the outset of your analysis.

NH: It is correct that theory based allometry was used at the outset to

guide the analysis. This was based not only the biological plausibility

of this theory but also the consistent use of non-linear weight scaling

in all previous reports of IV busulfan PK (see McCune Supplementary

Table 1). The results of non-linear regression using NONMEM are well

known to be better when starting from a priori more reasonable models

and parameters. A deeper understanding of the problem is always helpful.

SS:

2. I think your testing of this assumption is described on page 759:

“we estimated the allometric exponents for each of the 4 main

pharmacokinetic parameters (Supplementary Table S4). Initial estimates

of 2/3 and 1.25 were used for the clearance and volume exponents.”

However, you tested this with bootstrap, not with log-likelihood

profiles. Why?

NH:

A recognized limitation of log-likelihood profiles is the focus on just

one parameter at a time plus interpretation of the confidence interval

is dependent on the assumption that the difference in -2LL is

Chi-squared distributed. As I am sure you know that is a questionable

assumption when using the NONMEM approximation to the likelihood.

While the bootstrap cannot be considered perfect it has useful

properties compared with log-likelihood profiles because it allows the

uncertainty for all exponents to be estimated simultaneously. The

log-likelihood profile method provides a rather superficial view because

it only allows the uncertainty for one parameter at time while fixing

other parameters at some other values.

SS:

3. If allometry makes little difference, then it is an expected

result that your final estimates would be close to the starting

parameters. This might especially be the case where there are 10

parameters in the calculation of clearance (see item 10 below),

compromising the “navigability” of the model away from the starting

estimate of PWR when the other 9 parameters start at the value

determined by assuming that PWR=0.75.

NH: The initial estimates for the bootstrap were deliberately set to

values that were quite distant from the theory based values (page 759,

para 1). This would be expected to allow the exponent estimates to

“navigate” more freely. As you point out it is possible that there would

be some kind of “memory” in the other parameters of the model determined

using theory based exponents.This is a good idea. I have tried to test

it by fitting the data with initial estimates assuming that total body

weight is the allometric mass with an allometric exponent for CL and V

parameters equal to 1 (linear weight model). The results of such a fit

should have no “memory” of theory based values. I then refit the data

starting from the final estimates of this linear weight model and

estimated the allometric exponents for CL, V, Q and V2 (empirical

allometric model). The bootstrap confidence intervals for these

exponents estimated from the empirical allometric model with total body

weight are shown here:

Parameter

Description

Bootstrap Average

2.5% ile

97.5% ile

Bootstrap RSE

PWR_CL

Allometric exponent for CL

0.764

0.733

0.798

2.3%

PWR_V

Allometric exponent for V1

1.011

0.871

1.115

5.6%

PWR_Q

Allometric exponent for Q

0.838

0.734

0.957

6.7%

PWR_V2

Allometric exponent for V2

0.930

0.885

0.988

2.6%

It is clear that the exponent estimates for CL and V consistent with

theory based allometry and inconsistent with a linear weight model. Not

accounting for body composition probably explains why the confidence

interval for V2 just misses the theory based prediction. This is not due

to a “memory” problem because very similar results were obtained

starting from theory based initial estimates and total body weight as

shown in McCune supplementary table 4.

The objective function value (OFV) difference between the linear model

and the empirical allometric model is 532.12 with 4 estimated

parameters. This difference in OFV would usually be interpreted to show

that the non-linear allometric model is superior to the linear function

of weight. This is letting the data speak and it is shouting out that

the linear model is inconsistent with the data.

SS:

4. I stated in my comments that allometric theory did not account for

the upper extreme of obesity. You agree, since you found it necessary to

corrected allometric scaling with an additional parameter to account for

the effects of obesity.

NH: I am happy to see that we agree that “obesity” is not part of theory

based allometry. However, please recognise that the mass associated with

“obesity” would be expected under theory based allometry to have an

influence. A deeper, biological question is what is this mass? The West

et al.theory does not specify how to account for mass, such as excess

fat, that probably has metabolic properties different from mass with

“normal” body composition. The NFM method estimates the combination of

fat free mass and fat mass that best agrees with allometric theory. The

assumption of allometric theory then allows insights into the

contributions of these components to “normal” allometric size.

SS:

5. I stated in my comments that allometric theory did not account for

maturation. You agree, since you found it necessary to add an additional

parameter for maturation.

NH: I am very happy to see that we agree that allometric theory does not

account for maturation. That is why a separate model component (with 2

parameters TM50CL and HIllCL) is included to account for maturation of

clearance.

SS:

6. You had actual body weight for only 133 subjects in this study, of

which only 24 subjects were less than 18 years of age (supplementary

table 2). Although your model has 1610 individuals, you only estimated

the allometric portion of your model from 24 children. This allometric

scaling parameter was assumed to be true for all 1407 subjects

(calculated from supplementary table 2). Since your allometric

parameter, Ffat, was derived from just 24 children, and applied to all

1407 children, your testing (supplementary table S4) may be a tautology.

NH: It is indeed a limitation of this data analysis that most of the

hospitals who contributed data did not supply actual body weight but a

“dosing weight” (see below). Ffat contributes to the allometric part of

the model but recall that allometric theory does not include maturation.

The Ffat parameters were estimated from all 133 subjects , irrespective

of age, with actual body weight recorded. Therefore I do not agree with

your assertion that I “only estimated the allometric portion of your

model from 24 children”.

SS:

7. You state on page 755 that you used the dosing weight in reference

18. Reference 18 is Gibbs, et al, The Impact of Obesity and Disease on

Busulfan Oral Clearance in Adults, Blood 1999;93:4436-40. Reference 18

discusses actual body weight, body surface area, adjusted ideal body

weight, and ideal body weight, all calculated from standard formulae.

There is no reference to Dosing Weight in this publication.

NH: You are correct. There is no reference describing DWT for patients

outside Seattle. This is because the method used to calculate DWT was

calculated using each institution’s own practice (see page 755, col 2,

end of 2nd paragraph describing the study population). The exact method

was not supplied with the data provided for each patient by the

institution. The dosing weight in Seattle was not used for model

development because actual body weight was recorded.

SS:

8. Dennis pointed out the potential safety concerns of allometric

scaling. I suggest that interested readers look at page 756 of your

paper. If that does not scare clinicians, then the exact math for dose

calculation appears in supplementary table 7. Would you be comfortable

if the oncologist treating your child had to calculate dose based on the

complex, interlocking equations required to estimate body size? What

theoretical advantage in dose calculation justifies the potential for

computational error inherent in supplementary table 7? The risk vs.

benefit of allometric scaling cannot be determined from the data in the

paper.

NH: You bring up an interesting issue that was never the subject of this

paper.Unfortunately, the literature abounds with evidence that doctors

e.g. anesthetists (Nanji, Patel et al. 2016), often make dosing errors.

My work with allometric scaling applied to prediction of clearance and

dosing is not an ivory tower activity.Safe dosing of dangerous medicines

requires good science and validated methods to ensure the correct dose

is administered.

The calculation of the dose for busulfan is complex. This is the only

drug I know of where the FDA has recommended detailed dose

individualization including calculation of an AUC in order to use the

drug (FDA 2015). At the request of my clinical colleagues in Auckland, I

was involved in the implementation and testing of a tool to guide

busulfan dosing in children and adults. The tool was initially based on

an FDA study (Booth, Rahman et al. 2007) describing an allometrically

scaled model for clearance and was subsequently updated using the

results in the McCune paper when an audit showed the predictions were

better. The web based dosing tool (www.nextdose.org) has been in use for

over 4 years to guide dosing of all patients in New Zealand receiving

high dose busulfan for bone marrow ablation. The tool is available for

use by anybody who has access to the internet. I understand that the

model will be used to guide dosing of all patients in the USA who have

samples submitted to the national laboratory in Seattle for measurement

of busulfan concentrations.

It is my personal hope that dosing decisions will be taken out of the

hands of doctors who rarely recognize the principles of rational dosing

and continue to use ad hoc empirical methods.

To quote from your “Allometry, Shallometry!” editorial, with an example

based on what you claim is a simple approach using the linear weight

model: “It is OK if you skipped the math. As a clinician, all you need

to know is the punchline”. You have been a pioneer in this area with

target controlled infusions so I don’t think I have to convince you that

this is the way of the future. Doctors should be responsible for

providing the data to decide on an appropriate dose and after that a

science based computation tool should work out the dose.

SS:

9. You have no data showing how well your model predicts individual

patients. The closest you come are the visual predictive checks (figure

1) and the prediction corrected visual predictive check (supplement 2).

This tells me that the cloud of points is about right. That’s fine, but

the average patient does not die. It is patient at the extremes of

prediction accuracy who are at increased risk. The data, as presented,

does not provide this information.

NH: This paper is based on pharmacokinetic data. There is no

effectiveness or safety data to judge risk. However, we have described

the expected fraction of patients that would be expected to be within an

acceptable range of concentrations using a predicted initial dose. Our

model performs better than other methods in nearly all the scenarios we

tested and is never worse to a clinically important degree. As noted

above a web based dosing system using this approach has been used by

clinicians in Auckland for over 4 years.

SS:

10. Clearance (page 757) is calculated 10 parameters:

a population estimate, which is adjusted for F(size), F(maturation), and

F(sex). F(size) is based on dosing weight (not explained, see 7 above),

height, WHS(50), WHS(max), F(fat), FFEM(DW), and PWR (your allometric

parameter, fixed at ¾). F(maturation) is based on PMA, TM(50), and the

Hill coefficient. F(sex) is a further adjustment for sex. When clearance

is a function of 10 parameters, I do not see how this tests allometric

scaling. Indeed, if allometric scaling were hurting your fit (unlikely –

more likely it makes no difference, see below), other parameters might

compensate to fit the data.

NH: Please look at Table 2 to count the parameters in the fixed effect

model. There are 12 estimated parameters. The number of parameters is

not a “test of allometric scaling”. It is a measure of the complexity of

variability of busulfan PK. These parameters identify predictable

sources of variability that can be used to aid initial dosing.

SS:

11. You compare this model to models by Trame, Paci,

and Bartelink, noting that your model performs much better than these

models. You are comparing your model with 12 structural parameters to

models with 2 (Trame), 4 (Paci), and 5 (Bartelink) structural

parameters. Your 12 parameter model better described your data than

these simpler structural models fit to your data. Did you expect

anything else?

NH: I certainly expected to find our model would do better because it

has a stronger mechanistic and biological basis. It is more complex than

others because it goes more deeply into biological understanding and

does better over a wide range of human size and age.

SS:

12. You state on page 762: “The model is based on

principles that have already been shown to be robust for predictions

with other small molecule agents from neonates to adults.” I don’t see

that. If “robust” means that it allometric helps describe PK at the

extremes of weight, then the allometric model was not robust. It

required adjustments for both maturation and for obesity. Between these

extremes, say 30-100 kg, any optimal coefficient times weight to the ¾

power will differ by less than 10% from an optimal coefficient times

weight alone. This will be invisible given the order of magnitude

variability in clearance (your figure 2).

NH: Robust refers to principles which recognize the major role of size

and maturation (the key components of our model) in explaining

variability in PK for many drugs (see (Holford, Heo et al. 2013)).The

influence of body composition as a predictor of allometric size has

fewer examples but it is only by digging below the surface that we can

discover new things and evaluate their importance.

It is no surprised that over a narrow range (30-100 kg) a linear model

is a reasonable approximation to theory based allometry. But this is not

true over the range of TBW (3 to 140 kg; see Figure 1) in the patients

in this study (see below).

SS:

I see little to no evidence that your paper with Dr. McCune demonstrated

superiority of allometry. Rather, your paper demonstrated that even a

model with 12 parameters could not reduce the variability of busulfan

estimated clearance beyond an order of magnitude.

NH: If the model can predict how to reduce variability by an order of

magnitude for a very toxic drug such as busulfan then I think this is a

major advance. It makes no difference how many parameters are needed.

The important thing is to be able to predict differences in PK which can

then be applied to achieve safe and effective dosing. If this was my

child faced with a bone marrow transplant I would want to use every

means possible to improve the chances of a successful graft and reduce

the substantial risk of serious toxicity and death.

The simulations you provide in your “Allometry, Shallometry!” editorial

replicate what I demonstrated 20 years ago (Holford 1996). I pointed out

at that time the underestimation of doses predicted from adults if a

linear weight model was assumed. You appear to propose using the same

mg/kg dose in a children as in adults for computational convenience. But

clinically recommended dosing regimens for busulfan use a higher mg/kg

dose in younger and lighter children with lower mg/kg doses for older

and heavier children. The allometric and maturation model we have

developed predicts and explains this pattern of mg/kg dosing

recommendations for busulfan and all other drugs used in humans

(Holford, Heo et al. 2013).

SS:

You also demonstrated that allometric models require specific

adjustments for maturation and dosing. You will recall this was one of

the points that I made in my comments, which are also discussed in the

Allometry Shallomatry! editorial.

NH: I think we are in agreement that theory based allometry can only

explain variability due to differences in body mass. Other factors also

explain variability such as maturation, organ function, drug

interactions, genotypes, etc. These factors have no influence on the

allometric component of the model. I do not agree with you when you say

that allometric models requires “specific adjustments” using factors

such as maturation. If you tried to understand more deeply the

allometric model you would realize it is not based on these other factors.

SS:

Perhaps there are other analyses of these data that would demonstrate a

significant benefit of allometric scaling of data. If you are willing to

share with me your data on the 133 subjects for whom you have actual

body weights, I would be happy to address the question directly.

NH: I understand that Jeannine McCune has contacted you and offered to

work with you to obtain permission to use the data.

SS:

Respectfully,

Steve

--

Steven L. Shafer, MD

Professor of Anesthesiology, Perioperative and Pain Medicine, Stanford

University

Adjunct Associate Professor of Bioengineering and Therapeutic Sciences, UCSF

NH: References

Booth, B. P., A. Rahman, R. Dagher, D. Griebel, S. Lennon, D. Fuller, C.

Sahajwalla, M. Mehta and J. V. Gobburu (2007). "Population

pharmacokinetic-based dosing of intravenous busulfan in pediatric

patients." _J Clin Pharmacol_ *47*(1): 101-111.

FDA (2015). "Busulfex Product Label

http://www.accessdata.fda.gov/drugsatfda_docs/label/2015/020954s014lbl.pdf."

Holford, N., Y. A. Heo and B. Anderson (2013). "A pharmacokinetic

standard for babies and adults." _J Pharm Sci_ *102*(9): 2941-2952.

Holford, N. H. (1996). "A size standard for pharmacokinetics." _Clin

Pharmacokinet_ *30*(5): 329-332.

Nanji, K. C., A. Patel, S. Shaikh, D. L. Seger and D. W. Bates (2016).

"Evaluation of Perioperative Medication Errors and Adverse Drug Events."

_Anesthesiology_ *124*(1): 25-34.

--

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(6)62 32 46 72

email:n.holford_at_auckland.ac.nz

http://holford.fmhs.auckland.ac.nz/

"Declarative languages are a form of dementia -- they have no memory of events"

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.

Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol. 2015;79(1):18-27.

Received on Wed Jun 01 2016 - 04:27:04 EDT

Date: Wed, 1 Jun 2016 10:27:04 +0200

Dear Steve,

Thanks for your responses of 22 May and 24 May PDT. Due to some

unexplained technical problem I have not been receiving posts from

PharmPK since 23 May and only just became aware of your 24 May post. I

have tried twice to post a response to PharmPK but it has not appeared

on the list as far as I can tell. I am therefore transferring this

discussion to nmusers.

On 22 May you wrote “I am not aware of any theory that supports scaling

by weight to the 3/4 power WITHIN A SPECIES”. Having read the 22 May

post from Douglas Eleveld and my own reply do you now accept that the

theory of West et al. supports 3/4 power weight scaling within a species

including humans?

My comments below are in response to your PharmPK post of 24 May.

Best wishes,

Nick

SS:

Dear Nick:

You stated in your comments to me, both on NMUSERS and on PHARMPK, that

a paper of yours with Dr. McCune offered a validation of the use of

allometric scaling. Dennis Fisher has already commented on this paper.

Dennis said I might have additional comments. As usual, Dennis is right.

The paper is McCune et al, Busulfan in infant to adult hematopoietic

cell transplant recipients: a population pharmacokinetic model for

initial and Bayesian dose personalization.. Clin Cancer Res.

2014;20:754-63. Based on my reading of your paper, and the supplementary

material, I would like to offer several observations.

1. Quoting from page 755: “To characterize busulfan pharmacokinetics

over the entire age continuum, all clearance (CL,Q) and volume (V1, V2)

parameters were scaled for body size and composition using allometric

theory and predicted fat-free mass.” In other words, you assumed

allometric theory at the outset of your analysis.

NH: It is correct that theory based allometry was used at the outset to

guide the analysis. This was based not only the biological plausibility

of this theory but also the consistent use of non-linear weight scaling

in all previous reports of IV busulfan PK (see McCune Supplementary

Table 1). The results of non-linear regression using NONMEM are well

known to be better when starting from a priori more reasonable models

and parameters. A deeper understanding of the problem is always helpful.

SS:

2. I think your testing of this assumption is described on page 759:

“we estimated the allometric exponents for each of the 4 main

pharmacokinetic parameters (Supplementary Table S4). Initial estimates

of 2/3 and 1.25 were used for the clearance and volume exponents.”

However, you tested this with bootstrap, not with log-likelihood

profiles. Why?

NH:

A recognized limitation of log-likelihood profiles is the focus on just

one parameter at a time plus interpretation of the confidence interval

is dependent on the assumption that the difference in -2LL is

Chi-squared distributed. As I am sure you know that is a questionable

assumption when using the NONMEM approximation to the likelihood.

While the bootstrap cannot be considered perfect it has useful

properties compared with log-likelihood profiles because it allows the

uncertainty for all exponents to be estimated simultaneously. The

log-likelihood profile method provides a rather superficial view because

it only allows the uncertainty for one parameter at time while fixing

other parameters at some other values.

SS:

3. If allometry makes little difference, then it is an expected

result that your final estimates would be close to the starting

parameters. This might especially be the case where there are 10

parameters in the calculation of clearance (see item 10 below),

compromising the “navigability” of the model away from the starting

estimate of PWR when the other 9 parameters start at the value

determined by assuming that PWR=0.75.

NH: The initial estimates for the bootstrap were deliberately set to

values that were quite distant from the theory based values (page 759,

para 1). This would be expected to allow the exponent estimates to

“navigate” more freely. As you point out it is possible that there would

be some kind of “memory” in the other parameters of the model determined

using theory based exponents.This is a good idea. I have tried to test

it by fitting the data with initial estimates assuming that total body

weight is the allometric mass with an allometric exponent for CL and V

parameters equal to 1 (linear weight model). The results of such a fit

should have no “memory” of theory based values. I then refit the data

starting from the final estimates of this linear weight model and

estimated the allometric exponents for CL, V, Q and V2 (empirical

allometric model). The bootstrap confidence intervals for these

exponents estimated from the empirical allometric model with total body

weight are shown here:

Parameter

Description

Bootstrap Average

2.5% ile

97.5% ile

Bootstrap RSE

PWR_CL

Allometric exponent for CL

0.764

0.733

0.798

2.3%

PWR_V

Allometric exponent for V1

1.011

0.871

1.115

5.6%

PWR_Q

Allometric exponent for Q

0.838

0.734

0.957

6.7%

PWR_V2

Allometric exponent for V2

0.930

0.885

0.988

2.6%

It is clear that the exponent estimates for CL and V consistent with

theory based allometry and inconsistent with a linear weight model. Not

accounting for body composition probably explains why the confidence

interval for V2 just misses the theory based prediction. This is not due

to a “memory” problem because very similar results were obtained

starting from theory based initial estimates and total body weight as

shown in McCune supplementary table 4.

The objective function value (OFV) difference between the linear model

and the empirical allometric model is 532.12 with 4 estimated

parameters. This difference in OFV would usually be interpreted to show

that the non-linear allometric model is superior to the linear function

of weight. This is letting the data speak and it is shouting out that

the linear model is inconsistent with the data.

SS:

4. I stated in my comments that allometric theory did not account for

the upper extreme of obesity. You agree, since you found it necessary to

corrected allometric scaling with an additional parameter to account for

the effects of obesity.

NH: I am happy to see that we agree that “obesity” is not part of theory

based allometry. However, please recognise that the mass associated with

“obesity” would be expected under theory based allometry to have an

influence. A deeper, biological question is what is this mass? The West

et al.theory does not specify how to account for mass, such as excess

fat, that probably has metabolic properties different from mass with

“normal” body composition. The NFM method estimates the combination of

fat free mass and fat mass that best agrees with allometric theory. The

assumption of allometric theory then allows insights into the

contributions of these components to “normal” allometric size.

SS:

5. I stated in my comments that allometric theory did not account for

maturation. You agree, since you found it necessary to add an additional

parameter for maturation.

NH: I am very happy to see that we agree that allometric theory does not

account for maturation. That is why a separate model component (with 2

parameters TM50CL and HIllCL) is included to account for maturation of

clearance.

SS:

6. You had actual body weight for only 133 subjects in this study, of

which only 24 subjects were less than 18 years of age (supplementary

table 2). Although your model has 1610 individuals, you only estimated

the allometric portion of your model from 24 children. This allometric

scaling parameter was assumed to be true for all 1407 subjects

(calculated from supplementary table 2). Since your allometric

parameter, Ffat, was derived from just 24 children, and applied to all

1407 children, your testing (supplementary table S4) may be a tautology.

NH: It is indeed a limitation of this data analysis that most of the

hospitals who contributed data did not supply actual body weight but a

“dosing weight” (see below). Ffat contributes to the allometric part of

the model but recall that allometric theory does not include maturation.

The Ffat parameters were estimated from all 133 subjects , irrespective

of age, with actual body weight recorded. Therefore I do not agree with

your assertion that I “only estimated the allometric portion of your

model from 24 children”.

SS:

7. You state on page 755 that you used the dosing weight in reference

18. Reference 18 is Gibbs, et al, The Impact of Obesity and Disease on

Busulfan Oral Clearance in Adults, Blood 1999;93:4436-40. Reference 18

discusses actual body weight, body surface area, adjusted ideal body

weight, and ideal body weight, all calculated from standard formulae.

There is no reference to Dosing Weight in this publication.

NH: You are correct. There is no reference describing DWT for patients

outside Seattle. This is because the method used to calculate DWT was

calculated using each institution’s own practice (see page 755, col 2,

end of 2nd paragraph describing the study population). The exact method

was not supplied with the data provided for each patient by the

institution. The dosing weight in Seattle was not used for model

development because actual body weight was recorded.

SS:

8. Dennis pointed out the potential safety concerns of allometric

scaling. I suggest that interested readers look at page 756 of your

paper. If that does not scare clinicians, then the exact math for dose

calculation appears in supplementary table 7. Would you be comfortable

if the oncologist treating your child had to calculate dose based on the

complex, interlocking equations required to estimate body size? What

theoretical advantage in dose calculation justifies the potential for

computational error inherent in supplementary table 7? The risk vs.

benefit of allometric scaling cannot be determined from the data in the

paper.

NH: You bring up an interesting issue that was never the subject of this

paper.Unfortunately, the literature abounds with evidence that doctors

e.g. anesthetists (Nanji, Patel et al. 2016), often make dosing errors.

My work with allometric scaling applied to prediction of clearance and

dosing is not an ivory tower activity.Safe dosing of dangerous medicines

requires good science and validated methods to ensure the correct dose

is administered.

The calculation of the dose for busulfan is complex. This is the only

drug I know of where the FDA has recommended detailed dose

individualization including calculation of an AUC in order to use the

drug (FDA 2015). At the request of my clinical colleagues in Auckland, I

was involved in the implementation and testing of a tool to guide

busulfan dosing in children and adults. The tool was initially based on

an FDA study (Booth, Rahman et al. 2007) describing an allometrically

scaled model for clearance and was subsequently updated using the

results in the McCune paper when an audit showed the predictions were

better. The web based dosing tool (www.nextdose.org) has been in use for

over 4 years to guide dosing of all patients in New Zealand receiving

high dose busulfan for bone marrow ablation. The tool is available for

use by anybody who has access to the internet. I understand that the

model will be used to guide dosing of all patients in the USA who have

samples submitted to the national laboratory in Seattle for measurement

of busulfan concentrations.

It is my personal hope that dosing decisions will be taken out of the

hands of doctors who rarely recognize the principles of rational dosing

and continue to use ad hoc empirical methods.

To quote from your “Allometry, Shallometry!” editorial, with an example

based on what you claim is a simple approach using the linear weight

model: “It is OK if you skipped the math. As a clinician, all you need

to know is the punchline”. You have been a pioneer in this area with

target controlled infusions so I don’t think I have to convince you that

this is the way of the future. Doctors should be responsible for

providing the data to decide on an appropriate dose and after that a

science based computation tool should work out the dose.

SS:

9. You have no data showing how well your model predicts individual

patients. The closest you come are the visual predictive checks (figure

1) and the prediction corrected visual predictive check (supplement 2).

This tells me that the cloud of points is about right. That’s fine, but

the average patient does not die. It is patient at the extremes of

prediction accuracy who are at increased risk. The data, as presented,

does not provide this information.

NH: This paper is based on pharmacokinetic data. There is no

effectiveness or safety data to judge risk. However, we have described

the expected fraction of patients that would be expected to be within an

acceptable range of concentrations using a predicted initial dose. Our

model performs better than other methods in nearly all the scenarios we

tested and is never worse to a clinically important degree. As noted

above a web based dosing system using this approach has been used by

clinicians in Auckland for over 4 years.

SS:

10. Clearance (page 757) is calculated 10 parameters:

a population estimate, which is adjusted for F(size), F(maturation), and

F(sex). F(size) is based on dosing weight (not explained, see 7 above),

height, WHS(50), WHS(max), F(fat), FFEM(DW), and PWR (your allometric

parameter, fixed at ¾). F(maturation) is based on PMA, TM(50), and the

Hill coefficient. F(sex) is a further adjustment for sex. When clearance

is a function of 10 parameters, I do not see how this tests allometric

scaling. Indeed, if allometric scaling were hurting your fit (unlikely –

more likely it makes no difference, see below), other parameters might

compensate to fit the data.

NH: Please look at Table 2 to count the parameters in the fixed effect

model. There are 12 estimated parameters. The number of parameters is

not a “test of allometric scaling”. It is a measure of the complexity of

variability of busulfan PK. These parameters identify predictable

sources of variability that can be used to aid initial dosing.

SS:

11. You compare this model to models by Trame, Paci,

and Bartelink, noting that your model performs much better than these

models. You are comparing your model with 12 structural parameters to

models with 2 (Trame), 4 (Paci), and 5 (Bartelink) structural

parameters. Your 12 parameter model better described your data than

these simpler structural models fit to your data. Did you expect

anything else?

NH: I certainly expected to find our model would do better because it

has a stronger mechanistic and biological basis. It is more complex than

others because it goes more deeply into biological understanding and

does better over a wide range of human size and age.

SS:

12. You state on page 762: “The model is based on

principles that have already been shown to be robust for predictions

with other small molecule agents from neonates to adults.” I don’t see

that. If “robust” means that it allometric helps describe PK at the

extremes of weight, then the allometric model was not robust. It

required adjustments for both maturation and for obesity. Between these

extremes, say 30-100 kg, any optimal coefficient times weight to the ¾

power will differ by less than 10% from an optimal coefficient times

weight alone. This will be invisible given the order of magnitude

variability in clearance (your figure 2).

NH: Robust refers to principles which recognize the major role of size

and maturation (the key components of our model) in explaining

variability in PK for many drugs (see (Holford, Heo et al. 2013)).The

influence of body composition as a predictor of allometric size has

fewer examples but it is only by digging below the surface that we can

discover new things and evaluate their importance.

It is no surprised that over a narrow range (30-100 kg) a linear model

is a reasonable approximation to theory based allometry. But this is not

true over the range of TBW (3 to 140 kg; see Figure 1) in the patients

in this study (see below).

SS:

I see little to no evidence that your paper with Dr. McCune demonstrated

superiority of allometry. Rather, your paper demonstrated that even a

model with 12 parameters could not reduce the variability of busulfan

estimated clearance beyond an order of magnitude.

NH: If the model can predict how to reduce variability by an order of

magnitude for a very toxic drug such as busulfan then I think this is a

major advance. It makes no difference how many parameters are needed.

The important thing is to be able to predict differences in PK which can

then be applied to achieve safe and effective dosing. If this was my

child faced with a bone marrow transplant I would want to use every

means possible to improve the chances of a successful graft and reduce

the substantial risk of serious toxicity and death.

The simulations you provide in your “Allometry, Shallometry!” editorial

replicate what I demonstrated 20 years ago (Holford 1996). I pointed out

at that time the underestimation of doses predicted from adults if a

linear weight model was assumed. You appear to propose using the same

mg/kg dose in a children as in adults for computational convenience. But

clinically recommended dosing regimens for busulfan use a higher mg/kg

dose in younger and lighter children with lower mg/kg doses for older

and heavier children. The allometric and maturation model we have

developed predicts and explains this pattern of mg/kg dosing

recommendations for busulfan and all other drugs used in humans

(Holford, Heo et al. 2013).

SS:

You also demonstrated that allometric models require specific

adjustments for maturation and dosing. You will recall this was one of

the points that I made in my comments, which are also discussed in the

Allometry Shallomatry! editorial.

NH: I think we are in agreement that theory based allometry can only

explain variability due to differences in body mass. Other factors also

explain variability such as maturation, organ function, drug

interactions, genotypes, etc. These factors have no influence on the

allometric component of the model. I do not agree with you when you say

that allometric models requires “specific adjustments” using factors

such as maturation. If you tried to understand more deeply the

allometric model you would realize it is not based on these other factors.

SS:

Perhaps there are other analyses of these data that would demonstrate a

significant benefit of allometric scaling of data. If you are willing to

share with me your data on the 133 subjects for whom you have actual

body weights, I would be happy to address the question directly.

NH: I understand that Jeannine McCune has contacted you and offered to

work with you to obtain permission to use the data.

SS:

Respectfully,

Steve

--

Steven L. Shafer, MD

Professor of Anesthesiology, Perioperative and Pain Medicine, Stanford

University

Adjunct Associate Professor of Bioengineering and Therapeutic Sciences, UCSF

NH: References

Booth, B. P., A. Rahman, R. Dagher, D. Griebel, S. Lennon, D. Fuller, C.

Sahajwalla, M. Mehta and J. V. Gobburu (2007). "Population

pharmacokinetic-based dosing of intravenous busulfan in pediatric

patients." _J Clin Pharmacol_ *47*(1): 101-111.

FDA (2015). "Busulfex Product Label

http://www.accessdata.fda.gov/drugsatfda_docs/label/2015/020954s014lbl.pdf."

Holford, N., Y. A. Heo and B. Anderson (2013). "A pharmacokinetic

standard for babies and adults." _J Pharm Sci_ *102*(9): 2941-2952.

Holford, N. H. (1996). "A size standard for pharmacokinetics." _Clin

Pharmacokinet_ *30*(5): 329-332.

Nanji, K. C., A. Patel, S. Shaikh, D. L. Seger and D. W. Bates (2016).

"Evaluation of Perioperative Medication Errors and Adverse Drug Events."

_Anesthesiology_ *124*(1): 25-34.

--

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(6)62 32 46 72

email:n.holford_at_auckland.ac.nz

http://holford.fmhs.auckland.ac.nz/

"Declarative languages are a form of dementia -- they have no memory of events"

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.

Holford N. Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol. 2015;79(1):18-27.

Received on Wed Jun 01 2016 - 04:27:04 EDT