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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.

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Round table: Principle of dosage selection for veterinary pharmaceutical productsBayesian 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

why a bayesian forecasting method

Efficacy

Toxicity

Exposure

Why a bayesian forecasting method ?

Consequence of PK Variability :

the same dose gives different exposures

why a bayesian forecasting method1

Efficacy

Toxicity

Exposure

Why a bayesian forecasting method ?

Consequence of PK Variability :

the same dose gives different exposures

We need to anticipate the "level" of exposure

how to predict exposure1

POPULATION PK

Cannot be predicted with covariates

Need further information

Exposure

Covariate : e.g. Age

How to predict exposure ?
the bayesian approach

a priori information

A blood sample at this time

The bayesian approach

Same dose

animals with the same age

Probably a high exposure

the bayesian approach1

Probably a small exposure

A blood sample at this time

The bayesian approach

Same dose

animals with the same age

a priori information

the bayesian approach2

Exposure ?

A blood sample at this time

The bayesian approach

Same dose

animals with the same age

a priori information

why population information is needed
Why population information is needed ?

Concentration

Exposure ?

Time

A blood sample at this time

the bayesian approach3

A blood sample at this time

The bayesian approach

Same dose

animals with the same age

the bayesian approach4

Frequency

Exposure

A blood sample at this time

The bayesian approach

Same dose

animals with the same age

the a posteriori distribution
The a posteriori distribution

Distribution of exposure for animals that received the same dose

have the same age

have the same drug concentation at the sampling time

Frequency

Exposure

Maximum a posteriori (MAP)

= Bayesian estimate = most common exposure

the a priori information

Frequency

Exposure

The a priori information

Same dose

animals with the same age

A blood sample at this time

the a priori information1

Frequency

Exposure

The a priori information

Same dose

animals with the same age

A blood sample at this time

the a priori information2

Frequency

Exposure

The a priori information

Same dose

animals with the same age

A blood sample at this time

how to predict exposure2

Exposure

Covariate : e.g. Age

How to predict exposure ?

POP. PK

how to predict exposure3

Exposure

Covariate : e.g. Age

How to predict exposure ?

POP. PK + 1 concentration

POP. PK

how to predict exposure4

Exposure

Covariate : e.g. Age

How to predict exposure ?

POP. PK + 2 concentrations

POP. PK + 1 concentration

POP. PK

problem of highly variable drugs
Problem of highly variable drugs ?

1st Administration: fixed dose

Concentration

A blood sample at this time

Time

problem of highly variable drugs1
Problem of highly variable drugs ?

2nd Administration: same animal, same dose as 1st

Large inter-occasion variability

Concentration

A blood sample at this time

Time

how does it work
How does it work ?

A population model

jth concentration measured on the ithanimal

jth sample time of the ithanimal

how does it work1
How does it work ?

A set of concentrations on THE animal :

(t1, Z1), (t2, Z2), …

Maximize the a posteriori likelihood

Minimize

to summarize
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