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