Round table: Principle of dosage selection for veterinary pharmaceutical products Bayesian approach in dosage selection NATIONAL VETERINARY S C H O O L T O U L O U S E D. Concordet National Veterinary School Toulouse, France EAVPT Torino September 2006
Round table: Principle of dosage selection for veterinary pharmaceutical products Bayesian approach in dosage selection NATIONAL VETERINARY S C H O O L.
Dec 22, 2015
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Round table: Principle of dosage selection for veterinary pharmaceutical products
Bayesian approach in dosage selection
NATIONALVETERINARYS C H O O L
T O U L O U S E
D. ConcordetNational Veterinary School
Toulouse, France
EAVPT Torino September 2006
Bayesian forecasting methods =
Therapeutic drug monitoring
Why a bayesian forecasting method ?
Consequence of PK Variability :
the same dose gives different exposures
Exposure
Eff
icac
y Toxicity
Why a bayesian forecasting method ?
Consequence of PK Variability :
the same dose gives different exposures
Exposure
ToxicityE
ffic
acy We need to anticipate the "level" of exposure
How to predict exposure ?
Exposure
How to predict exposure ?E
xpos
ure
Covariate : e.g. Age
POPULATION PK
Cannot be predicted with covariatesNeed further information
Time
Co
nc
en
tra
tio
nThe bayesian approach
Same dose animals with the same age
A blood sample at this time
Probably a high exposure
a priori information
Time
Co
nc
en
tra
tio
nThe bayesian approach
Same dose animals with the same age
A blood sample at this time
Probably a small exposure
a priori information
Time
Co
nc
en
tra
tio
nThe bayesian approach
Same dose animals with the same age
A blood sample at this time
Exposure ?
a priori information
Time
Co
nc
en
tra
tio
nWhy population information is
needed ?
A blood sample at this time
Exposure ?
Time
Co
nce
ntr
atio
n
The bayesian approach
Time
Co
nc
en
tra
tio
n
Same dose animals with the same age
A blood sample at this time
The bayesian approach
Time
Co
nc
en
tra
tio
n
Same dose animals with the same age
A blood sample at this time
Exposure
Fre
quen
cy
The a posteriori distribution
Distribution of exposure for animals that received the same dose
have the same agehave the same drug concentation at the sampling time
ExposureMaximum a posteriori (MAP)= Bayesian estimate = most common exposure
Fre
quen
cy
The a priori information
Time
Co
nc
en
tra
tio
n
Same dose animals with the same age
A blood sample at this time
Exposure
Fre
quen
cy
The a priori information
Time
Co
nc
en
tra
tio
n
Same dose animals with the same age
A blood sample at this time
Exposure
Fre
quen
cy
The a priori information
Time
Co
nc
en
tra
tio
n
Same dose animals with the same age
A blood sample at this time
Exposure
Fre
quen
cy
How to predict exposure ?E
xpos
ure
Covariate : e.g. Age
POP. PK
How to predict exposure ?E
xpos
ure
Covariate : e.g. Age
POP. PK
POP. PK + 1 concentration
How to predict exposure ?E
xpos
ure
Covariate : e.g. Age
POP. PK
POP. PK + 1 concentration
POP. PK + 2 concentrations
time
Problem of highly variable drugs ?
Time
Con
cent
ratio
n
1st Administration: fixed dose
A blood sample at this time
time
Problem of highly variable drugs ?
Large inter-occasion variability
Time
Con
cent
ratio
n
2nd Administration: same animal, same dose as 1st
A blood sample at this time
jitKatK
iii
iji
jiijii eeKKaV
DFY ,
10, 1,,10
How does it work ?
;~ ii AN
VVi
KKi
FiFi
KaKai
i
i
i
i
V
K
BWF
Ka
101010
jiY ,
jit ,
jth concentration measured on the ith animaljth sample time of the ith animal
A population model
jijiiji tfY ,,, 1,
How does it work ?
)(),()( PZPZP
A set of concentrations on THE animal : (t1, Z1) , (t2, Z2) , …
Maximize the a posteriori likelihood
Minimize
AAtf
tfZ t
i
ii
1
2
),(
),(
To summarize
Bayesian forecasting can be useful for:
pets
touchy drugs (narrow therapeutic index)
It requires:
results of a pop PK study
some concentrations on the animal
a recent computer
Can’t work for large inter-occasion variability
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