ECOLE
NATIONALE
VETERINAIRE
TOULOUSE
Allometric scaling to predict
pharmacokinetic and pharmacodynamic
parameters in man
PL Toutain
UMR 181 Physiopathologie et Toxicologie Expérimentales
INRA, ENVT
1
Introduction to allometry
Allometry (a term coined by Huxley
& Tessier 1936) is the study of size
and its consequences
2
Range of body size in mammals
Shrew 2 g
Blue whale: >108 g
Allometry is the study of size and its
consequences
• Interspecies allometric scaling is based on the
assumption that there are anatomical, physiological
and biochemical similarities among animals which
can be described by simple mathematical models
3
Range of body size in mammals:
extrapolation within species
Adult to adult
Young to adult
4
Many allometric relationships have been
established between body size and organ weight
as well as body size and physiological process
5
Simple allometry
y = 10x 0.6
R2 = 1
180
160
Y=aBWb
plasma clearance
140
120
100
80
60
40
20
0
0
20
40
60
80
100
120
Body weight
6
The power function
Y = aBWb
Where Y is the parameter of interest, BW is the body weight, a & b are
the coefficient and exponent of the allometric equation respectively
The log transformation of this equation is represented as :
log Y = log a + b x logBW
Linear plot: slope=b and intercept=log A
the slope of the line (b) indicates the type of scaling relationship
7
Simple allometry:
the log-log transformation
y = 10x 0.6
R2 = 1
1000
plasma clearance
logY=log a +b log BW
100
b=slope
10
Y=aBWb
1
0.01
log a is the Y-intercept
0.1
1
10
100
Body weight
8
The scaling exponent (b) i.e. the slope
defines the type of scaling relationship
12
parameter of interest
b=1.25
Y increase faster than BW
Positive allometry
10
8
6
b=1.0
4
Y increase proportionally
with BW (isometry)
2
b=0.75
0
0
2
4
6
8
Body weight
10
12
Y increase slower than BW
Negative allometry
9
The assumption behind the log-log
transformation
• It is assumed that there is a constant %CV
about the value of PK parameter
associated with BW being considered
10
The log-log transformation
•log-log transformation of the data will visually minimize
the deviations from a regression line
• A high R2 (e.g. 0.95) do not guarantee that all the data
point will be close to the regression line
•The extrapolation of this regression line to obtain a
predicted human value may have a great uncertainty
•The regression process does not treat the weight of
each animal species comparably
•Direct fitting of power function with incorporation of a
weighting strategy has been shown not to improve the
prediction performance
11
The log-log transformation
• When there is a limited number of species
associated with the regression analysis,
each data point has the greatest impact on
the prediction of Y for animals whose
value of BW are closer to the deviant
observation
12
• How does a the distribution of body weight used
in the regression analysis influence the
prediction of Y
• For any species included in the regression
analysis, how does its location on the X-axis (i.e;
its value of BW relative to other observed data
points) influence prediction of Y
• Can we anticipate the impact on prediction error
by the goodness of fit (R2) of the regression line
13
Number of species and the
regression line
• When there is a limited number of species associated
with the regression analysis, each data point has the
greatest impact on the prediction of Y for animals whose
value of BW are closest to the deviant observation
• When a midpoint species (dog in vet medecine) is the
source of the error, the change is primarily in the
intercept rather the slope; consequently the resulting
magnitude of prediction error is comparable throughout
the range of BW values examined
14
Influence on the predicted value in man of a 30% decrease
of the clearance value for a given species
species
BW (kg)
CL
CL
CL
CL
Mouse
0.03
0.72 8
0.72 8
0.72 8
0.5046
Rat
0.2
2.99
2.09
2.99
2.99
Rabbit
4
28.28
28.28
28.28
28.28
monkey
8
47.56
47.56
47.56
47.56
dog
15
76.21
76.21
54.25
76.21
Man
70
242
247
200
212
predicted
bias
0%
+2%
+17%
+12%
15
ACCURACY OF ALLOMETRICALLY PREDICTED PHARMACOKINETIC
PARAMETERS IN HUMANS: ROLE OF SPECIES SELECTION
Huadong Tang and Michael Mayersohn
16
Drug Metabolism Disposition, 2005, 33 (9) 1288-1293
ACCURACY OF ALLOMETRICALLY PREDICTED PHARMACOKINETIC
PARAMETERS IN HUMANS: ROLE OF SPECIES SELECTION
Huadong Tang and Michael Mayersohn
Drug Metabolism Disposition, 2005, 33 (9) 1288-1293
As demonstrated by both theoretical and literature experimentation,
rats had no significance in predicting human PK parameters as long as
the body weight of the rat is not the smallest in the species used in the
allometric relationship.
17
Historical developments:
the direct extrapolation of doses
from animals to man
18
The Use of Body Surface Area as a Criterion of
Drug Dosage in Cancer Chemotherapy
Donald Pinkel
(Department of Pediatrics, Ronwell Park Memorial Institute
and
University of Buffalo School of Medicine, Buffalo, N.Y.)
Cancer Res 1958 28 853-856
19
The use of body surface area as a criterion of
dosage regimen in cancer chemotherapy
(From D Pinkel :Cancer Res 1958 28 853-856)
Methotrexate
6
Methotrexate
5
y = 2.7102x + 0.0987
R2 = 0.9947
6
dose per day in mg
dose per day in mg
y = 0.3356x 0.642
R2 = 0.9989
4
3
2
1
0
0
10
20
30
40
50
60
70
80
Body weight
5
4
3
2
1
0
0
0.5
1
1.5
2
surface area
Mouse=0.018
y = 0.3356x
Methotrexate
0.642
2
R = 0.9989
Body weight in Kg
Infant=8
Rat=0.25
Child=20
Adult=70
dose per day in mg
10
1
0.1
0.01
0.01
0.1
1
Body weight
10
100
20
Body surface area in man
• The DuBois and DuBois formula
– BSA (m²) = 0.20247 x Height(m)0.725 x Weight(kg)0.425
• The Haycock formula
– BSA (m²) = 0.024265 x Height(cm)0.3964 x Weight(kg)0.5378
• The Gehan and George formula
– BSA (m²) = 0.0235 x Height(cm)0.42246 x Weight(kg)0.51456
• The Boyd formula
– BSA (m2) = 0.0003207 x Height(cm)0.3 x Weight(grams)(0.7285 - (
0.0188 x LOG(grams) )
21
Comparison of toxicity data acquired during clinical studies of
18 anticancer agents with those obtained in mice, rats, dogs,
and rhesus monkeys uncovered close interspecies
correlations when doses were related to body surface, much
closer than when doses were related to mass. This finding
has guided numerous trials of anticancer and other agents.
22
Comparison of toxicity data on anticancer agents for
the Swiss mouse and man (on a mg per m2 basis)
From Freireich et al 1966
Maximum tolerated dose (mg per m2)
1000
100
Antimetabolites
Alkylating agents
Others
10
1.0
0.1
10
Mouse LD10 mg per
1000
m2
23
Observed and predicted dosage (mg per m2) in
man using animal system (Freireich & al 1966)
24
Interspecies scaling of maximum
tolerated dose of anticancer drugs
• In general, small animal require larger dose than
human to reach the MTD.
• Wanatabe et al used the LD10 mice data from
25 anticancer drugs and concluded that the
MTD in human can be predicted from mice LD1
using a scaling power of 0.75
• Actually the use of a fixed exponent cannot be
justified
25
Slope actually from 0.60 to 0.84
Data from Freireich & al 1966
26
Body weight or body surface area?
• BSA is not directly measured but
estimated with allometric equations
• For a given species, it may exist several
equations predicting BSA
• There is no advantage using BSA over BW
27
28
What is exactly a Dose?
29
The determination of an ED50 or any ED%
PD
ED50 =
Clearance x target EC50
Bioavailability
PK
ED50 - is a hybrid parameter (PK and PD)
- is not a genuine PD drug parameter
30
What is a dose?
Cardiac _ output (L / day )  321  BW (kg )0.75
clearance plasma  Cardiac _ Output  ER
Dose 
clearance plasma  ECtherapeutical
Bioavailab ility
31
Cardiac output in mammals
Cardiac _ output  223  BW
In mL per minute
0.75
Body Weight in 32
kg
Interpretation of body clearance
• Interpretation of body clearance
consists of calculating an extraction
ratio
Ebody =
Body clearance (blood)
Cardiac output
33
What is a dose?
Cardiac output (L per day)
µg/L
Dose 
321  BW 0.75  ER  ECtherapeutical
Bioavailab ility
µg per day
34
Dose (IV) for an hepatic cleared drug with a low or
a high hepatic extraction ratio (ER)
Low ER
V max
Dose  fu 
 ECtherapeutical
Km
The plasma protein binding and metabolism activity are the major
determinants for the elimination of low hepatic clearance drugs;
therefore it is not expected to have a good allometric relationship
with BW across species for this kind of drug
High ER
Dose  68BW 0.76  ECtherapeutical
Because hepatic blood flow is shown to have an allometric
relationship with BW, it is expected that the elimination of high
hepatic clearance drug can show an allometric relationship with BW
35
Interspecies scaling of
pharmacodynamic parameters
PD
ED50 =
Clearance x target EC50
Bioavailability
36
Interspecies scaling of
pharmacodynamic parameters
• Very little information is available for the
prediction of pharmacodynamic (PD)
parameters from animal to man
• It is conceptually difficult to accept that the
efficacy and potency of a drug will relate
with body weight of the species
37
Allometry of pharmacokinetics and
pharmacodynamics of the muscle relaxant
metocurine in mammals
38
Interspecies scaling of
pharmacodynamic parameters:
The case of Ketoprofen (sKTP)
• Cat, goat, sheep, calf, horse
• Endpoints: inhibition of the synthesis of
thromboxan (TXB2) and prostaglandinE2
(PGE2)
• No relationship between IC50 (or other PD
parameters) with BW
39
Modeling and allometric scaling of s(+)-ketoprofen
pharmacokinetics and pharmacodynamics: a
retrospective analysis
E.-I. LEPIST & W.J. JUSKO, J. Vet. Pharmacol. Therap. 27, 211-218, 2004
ANTIINFLAMMATORY DRUG
40
41
Interspecies scaling of pharmacodynamic
parameters:
the case of anaesthetic potency minimum
alveolar concentration (MAC)
• Poor correlation between BW and MAC
for several inhalation anesthetics
•Travis & Bowers 1991in: Toxicol Ind Health 1991 7 249-260
42
In vitro data: Drug affinity & drug potency
Drug potency
from in vitro:
MIC for
antibiotics
Benzodiazepine dose and benzodiazepine affinity
43
Interspecies scaling of
pharmacokinetic parameters
ED50 =
Clearance x target EC50
Bioavailability
44
Volume of
distribution
Absorption
Clearance
bioavailability
Half-life
Dosing regimen
How often?
Systemic
exposure
Dosage regimen
How much 45
Acute toxicity of anticancer drugs
human versus mouse
AUC Ratio
Internal dose
Frequency
Dose Ratio
External dose
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0-1
0.4-0.6
0.6-1.2
2.0-3.0
>4
0
0-1
0.4-0.6
0.6-1.2
2.0-3.0
>4
46
Interspecies scaling of clearance
47
Simple allometry: Diazepam
48
Scaling of antipyrine intrinsic clearance in 15
mammalian species
y = 8.2911x 0.8922
R2 = 0.9713
antipyrine in mammals
Intrinsic clearance in mL per min
10000
1000
100
10
1
0.1
0.01
0.1
1
10
100
1000
Body weight in kg
Boxenbaum & Fertig Europ J Drug Metab Pharmacokinet 1984 9 177-183
49
The concept of neoteny
• Retention of juvenile
characteristics in the
adults of species
• The modern man
retained its juvenile
characteristics of its
ancestors (apes)
through the
retardation of somatic
development for
selected organs
50
Exemple of Neoteny
51
Interspecies scaling of clearance
1. Simple allometry
2. Allometry with various biological
correction factors
3.
4.
5.
6.
7.
1. Product of maximum life-span (MLP) and
clearance
2. Product of brain weight and clearance
Ratio of clearance and GFR
Two-term power equation
Incorporation of molecular structure parameters
incorporation of in-vitro data in in-vivo clearance
Correction for protein binding
52
Simple allometry & allometry with standard
correction factors (MLP and Brain weight)
• Clearance or Clearance multiplied by MLP or Brain
weight of several species are plotted against BW on
a log-log plot
Clearance  aBW
b
Clearance  MLP  aBW
b
Clearance  BrainWeigh t  aBW
b
53
Product of maximum life-span (MLP) and
clearance
• The clearance of different species are multiplied by
their respective MLP and are plotted against a
function of BW on a log-log scale
Clearance man
a(MLP  Clearance )

5
8.18  10
b
MLP(years )  185.4 * Brain _ weight 0.636 * BW 0.225
54
Prediction of Cefazolin Clearance in man:
standard vs. corrected allometry (MLP)
0.7828
Cefazolin y = 5.3801x
y = 3.7432x1.1068
R2 = 0.9906
cefazolin MLP
R2 = 0.9982
1000
1000
100
CL X MLP
Clearance
100
10
1
0.1
0.01
10
1
0.1
0.1
1
Body weight
Simple allometry
Predicted: 141 mL/min
Actual: 61 mL/min
Error: 131%
10
100
0.01
0.01
0.1
1
10
100
Body weight in kg
Allometry with MLP as a correcting factor
Predicted: 50.55mL/min
Actual: 61mL/min
Error:17.1%
55
Selection of a standard correction factor
and the so-called rule of the exponent
• The random use of the different correction factors is of
no practical value
• Mahmood & Balian 1996 investigated 40 drugs and
found that the exponent of the simple allometry ranged
from 0.35 to 1.39
• Based on these exponents ,it was found that there are
conditions under which only one of the three methods
can be used preferentially for reasonably accurate
prediction of clearance
Mahmood & Balian 1996 xenobiotica 26 887-895
56
The « rule of exponents »
to predict clearance in man
Mahmood & Balian 1996
1. 0.55 ≤ b <0.71 : no correction factor is
necessary
2. 0.71 ≤ b <1.00 MLP should be incorporated
into scaling method
3. B>1.00 Brain weight should be incorporated
into the scaling method
57
The « rule of exponents »
to predict clearance in man for 50 drugs
Methods
Simple allometry
% Mean absolute error
(MAE)
106
CL x MLP
40
CL x brain Weight
49
Rule of exponents
25
Mahmood In interspecies pharmacokinetic scaling 2005 pp49
58
A Comprehensive Analysis of the Role of
Correction Factors in the Allometric Predictivity of
Clearance from Rat, Dog, and Monkey to Humans
RAKESH NAGILLA, KEITH W. WARD
• 103 compounds investigated
• Standard allometry and allometry including various correction factor
(MLP, brain weight, GFR) were performed
• Scaling were performed on all compounds universally and on
segregated subset based on allometric exponent, clearance,
physicochemical properties etc
• 776 allometric combinations with 27913 outcomes were preformed
• A predicted-to-observed clearance ratio of 0.5 to twofold was
preselected as the criterion for predictive success
59
Nagilla & Ward JPS 2004
60
No correction
Brain weight
MLP
Rule of the exponents
61
Nagilla & Ward 2004
A Comprehensive Analysis of the Role of Correction
Factors in the Allometric Predictivity of Clearance from
Rat, Dog, and Monkey to Humans
• When all three species were utilized in scaling
using simple allometry, 48 of 103 compounds
yielded a ratio (predicted/observed) that was not
within twofold of the observed value
• Incorporation of the empirical correction factor
MLP or brain weight, either universally or
judiciously according to the rule of exponents,
failed to improve the predictive performance of
the method.
62
A Comprehensive Analysis of the Role of Correction
Factors in the Allometric Predictivity of Clearance from
Rat, Dog, and Monkey to Humans
• The success rate of allometric scaling
ranged from 18 to 53%
• None of the correction factor resulted in
substantially improved predictivity
• None of the methods attempted in this
study achieved a success rate greater
than that observed by simply estimating
human clearance based on monkey
hepatic extraction
63
% outliers
Influence of species, routes of elimination and correction factors
Nagilla & Ward 2004
0.5-to twofold window
64
Value of the allometric approach
• Conclusion: the prospective allometric
scaling , with or without correction factors,
represent a suboptimal technique for
estimating human clearance based on in
vivo preclinical data
• Nagilla & Ward J Pharmac Sci 2004 1à 25222534
66
See also Obach & al for the value of
allometry as a predictive tool
67
Correction factors for renally and biliary
excreted drugs
• Renally excreted drugs
Clearance / GFR  aBW b
• Biliary excreted drugs
Cl  Bile _ flow  aBW B
Cl  UDPGT  aBW b
UDPGT=UDP-glucuronyltransferase activity
68
Interspecies scaling of clearance
1.
2.
Simple allometry
Allometry with various biological correction factors
1.
2.
3.
4.
Product of maximum life-span (MLP) and clearance
Product of brain weight and clearance
Ratio of clearance and GFR
Two-term power equation
5. Incorporation of molecular structure
parameters
6.
7.
incorporation of in-vitro data in in-vivo clearance
Correction for protein binding
69
Incorporation of molecular structure
parameters
• Wajima et al. 2002 suggested to use descriptors of
drugs related to clearance to predict clearance in man
e.g.:
– Molecular Weight ,Calculated partition coefficient (c log P;
Number of hydrogen bound acceptors (Ha)…).
• Then using some types of regression (multiple linear
regression analysis, partial least square analysis or
artificial neuronal network), a regression equation can
be derived to predict clearance in man:
Log(CLman )  Log(CLrat )  Log(Cldog )  MW  Hydrogen _ bounding  ....
70
Interspecies scaling of clearance
1. Simple allometry
2. Allometry with various biological correction
factors
1. Product of maximum life-span (MLP) and clearance
2. Product of brain weight and clearance
3. Ratio of clearance and GFR
4. Two-term power equation
5. Incorporation of molecular structure
parameters
6. Correction for protein binding
7. incorporation of in-vitro data in in-vivo
clearance
71
Correction for protein binding
• Protein binding varies considerably among
animal species which in turn can influence the
distribution and elimination of drugs
• Theoretically unbound clearance should be
predicted with more accuracy than the total
clearance but in practical terms this is not the
case (Mahmood, 2005)
• Actually, the correction for binding simply adds
more variability to the unbound clearance of the
species
72
Interspecies scaling of clearance
1.
2.
Simple allometry
Allometry with various biological correction factors
1.
2.
3.
4.
5.
6.
Product of maximum life-span (MLP) and clearance
Product of brain weight and clearance
Ratio of clearance and GFR
Two-term power equation
Incorporation of molecular structure parameters
Correction for protein binding
7. incorporation of in-vitro data in invivo clearance
73
Dose for an hepatic cleared drug with a low
hepatic ER and a total absorption
V max
Dose  fu 
 ECtherapeutical
Km
The plasma protein binding and metabolism activity are the major
determinants for the elimination of low hepatic clearance drugs;
therefore it is not expected to have a good allometric relationship with
BW across species for this kind of drug as it is the case for antipyrine
( the Clint of antipyrine in man is only one-seventh of that which would
be predicted from other species)
74
Incorporation of in vitro data in in vivo
clearance (Lavé et al. 1997)
• Clearances are normalized with in vitro data
providing a more rational (mechanistic) approach for
predicting metabolic clearance in man
Clanimal 
CLhuman ( hepatocytes )
Clanimal ( hepatocytes )
 a  BW b
For 10 extensively metabolized compounds, adjusting the in vivo
clearance in the different animal species for the relative rates of
metabolism in vitro dramatically improved the prediction of human
clearance compared to the approach in which clearance is directly
extrapolated using BW
Lave et a., J Pham Sci., 1997, 86: 584-590
75
Interspecies Scaling of Bosentan, A New Endothelin
Receptor Antagonist and Integration of in vitro Data into
Allometric Scaling
Thierry Lave, Philippe Coassolo, Geneviève Ubeaud, Roger Brandt, Christophe Schmitt, Sylvie Dupin,
Daniel Jaeck ane Ruby C. Chou - Pharmaceutical Research, 13(1), 1996
Cl  a  BW b
R2=0.525
Predicted human clearance=196ml/min
Clanimal _ invivo 
Clhuman _ hepatocytes
Clanimal _ hepatocytes
R2=0.976
Predicted human clearance=100mL/min
77
Hepatocytes vs microsomes
• Absence of phase II metabolism on liver
microsomes, which could result in enzyme
inhibition due to the accumulation of the
oxidative metabolites
78
Incorporation of in-vitro data in invivo clearance
Methods
%MAE
Simple allometry
164
CL x Brain Weight
61
In-vitro method
40
Rule of exponent
38
Data of Lave al (J Pham Sci 1997 86 584-590) on 10 extensively
metabolised drugs reanalysd by Mahmood 2005
81
Extrapolation of bioavailability
82
Bioavailability in man:
prediction from rodents, primates & dogs ED%
ED50 =
Clearance x target EC50
Bioavailability
83
Absorption & Bioavailability (F)
%F  fabs  (1  fg )  (1  ERH )
where
fabs = fraction absorbed from GI lumen
fg = fraction metabolized by GI tissue
ERH = hepatic extraction ratio, equivalent
to hepatic “first pass” effect
1 - F = “presystemic elimination”
84
Bioavailability in man:
prediction from rodents, primates & dogs
85
From Grass ADDR 2002
Extrapolation of Vss
87
Interspecies scaling of volumes of
distribution (Vd)
Vss  Vp  Vt 
fup
fut
• Where Vp, is the volume of plasma; Vt is tissue
volume and fup and fut are the fraction of
unbound drug in plasma and tissues
respectively
• Usually a change in fut has a greater effect than
fup on Vss
88
The minimal volume of distribution is
7.5 L (0.1 L/kg)
• VD = 7.5 + 7.5 x fu + 27L x fu
p
fuT
Volume of
distribution of
albumin
Drug highly
bound to
No partitioning
plasma protein No tissue binding
fu=very smal
V = 7.5 L (not 3 L) which is the VD of albumin
Note: plasma volume = 3 L but plasma protein (and
drug) diffuse out of vascular space and thus protein
(and drug) will return through the lymphatic system
89
Interspecies scaling of volumes of
distribution (Vd)
• Because there is no allometric relationship
between protein binding and BW, it will be
difficult to project the Vd of drug in humans from
data in animals
• When a drug has a low binding to plasma and
tissue proteins or when a drug only distribute
extracellularly, the Vd of the drug reflect total
body water or extracellular water
– In these cases, the Vd in human can be predicted
from data in animals because both the total body
water and extracellular water decrease as animal size
increases in an allometric manner.
90
Volume of distribution of propranolol
Vtotal
Vfree (Unbound)
For propranonol, Vf should be similar in humans and other species
However this is not a general rule (e.g. large difference for Vf between
species for Beta-lactam antibiotics)
91
Interspecies scaling of volumes of
distribution (Vd)
• Vc is the most important volume parameter
which can be predicted with much more
accuracy than Vss or Vβ
• The exponent of all three volume revolve around
1.0 indicating that there exist a direct
relationship between BW and volume
• Correction for protein binding is not much help in
improving the prediction of vomume in man
92
Extrapolation of half-life
93
Interspecies scaling of elimination
half-life
• Application of HL to the first time dosing to
man is limited
• HL is an hybrid parameter (clearance and
Vd)
• Conceptually, it is difficult to establish a
relationship between HL and BW
• Unlike clearance and Vd , the correlation
of HL with BW has been found to be poor
94
R2=0.14
HL
CL
R2=0.90
R2=0.94
Allometric analysis of
ciprofloxacin half-life,
clearance and volume
of distribution across
mammals
Poor correlation for HL
while correlation for
CL and Vss are good
VD
95
96
Prediction of drug clearance in
children from adults
• Origin of the difference between children
and adults
– Variation in body composition
– Difference in liver and kidney function
97
Age-related changes clearance
Morphine
Fentanyl
98
Prediction of drug clearance in
children from adults
• 41 drugs considered
• 124 observations in children of different
age groups
• Infant, children, adolescent (from 1 day to
17 years)
Mahmood BJCP 2006
99
Tested models
1. Classical allometric equation with different exponents
CLin _ child
 BW child 
 Cladult  

BW
adult 

0.75 _ or _ 0.80 _ or _ 1.0
2. Correction of adult clearance by the estimated liver and
kidney weight in children
3. The clearance were estimated using a specific method for a
given age (decision tree)
• Child<1year: exponent=1
• Child >1 years but <5 years: correction by liver and kidney weight
• Child >5 years : allometric exponent of 0.75, 0.80 or 0.85
Mahmood BJCP 2006
100
Results
1. No single method was suitable for all
drugs or for all age groups
2. The %RMSE i.e. (MSE)0.5 was almost
similar for exponent 0.75, 0.80 and 0.85
as well as the approach based on the
liver and kidney weights
3. The lowest RMSE was seen with the
mixed approach
Mahmood BJCP 2006
101
Percent root mean square (RMSE) and percent error in the
prediction of clearance in children by several methods
Number of predictions in error
(>100%) for 124 predictions
Tested Exponents: 0.75, 0.89, 0.85 and 1.0
L+K: liver and kidney weights correction
Mixed : decision tree based upon age
Mahmood BJCP 2006
102
Children <1 year old
• The exponent 0.75 overpredicted the
clearance by several folds
• When exponent 1.0 (no exponent) was
used on the BW the prediction of
clearance was fairly reasonable and far
less erratic than 0.75
Mahmood BJCP 2006
103
Children from 1 to 5 years old
• The best approach appears to be the liver
and kidney weights corrections
Mahmood BJCP 2006
104
Children >5 years old
• One can use any exponent:
(0.75, 0.80 or 0.85)
Mahmood BJCP 2006
105
Allometry in veterinary medicine
106
107
108
Conclusions:
Advantages of interspecies PK scaling
• Simple and easy to use
• Require plasma concentration-time data from
which PK parameters are calculated
• Knowledge of elimination pathways, and plasma
protein binding may be helpful but not necessary
• Data analysis is short
• 80% success rate if incorporation of hepatocytes
information's
109
Limits of allometic scaling
110
111
Limits of allometric scaling
112
For more information, consult the
Mahmood’ book
113