Round table: Principle of dosage selection for veterinary pharmaceutical products Bayesian approach in dosage selection NATIONAL VETERINARY S C H O O L.

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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

Bayesian forecasting methods = Therapeutic drug monitoring

Why a bayesian forecasting method ? Consequence of PK Variability : the same dose gives different exposures Exposure Efficacy Toxicity

Why a bayesian forecasting method ? Consequence of PK Variability : the same dose gives different exposures Exposure Toxicity Efficacy We need to anticipate the "level" of exposure

How to predict exposure ? Exposure

How to predict exposure ? Exposure Covariate : e.g. Age POPULATION PK Cannot be predicted with covariates Need further information

The bayesian approach Same dose animals with the same age A blood sample at this time Probably a high exposure a priori information

The bayesian approach Same dose animals with the same age A blood sample at this time Probably a small exposure a priori information

The bayesian approach Same dose animals with the same age A blood sample at this time Exposure ? a priori information

Why population information is needed ? A blood sample at this time Exposure ? Time Concentration

The bayesian approach Same dose animals with the same age A blood sample at this time

The bayesian approach Same dose animals with the same age A blood sample at this time Exposure Frequency

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 Exposure Maximum a posteriori (MAP) = Bayesian estimate = most common exposure Frequency

The a priori information Same dose animals with the same age A blood sample at this time Exposure Frequency

The a priori information Same dose animals with the same age A blood sample at this time Exposure Frequency

The a priori information Same dose animals with the same age A blood sample at this time Exposure Frequency

How to predict exposure ? Exposure Covariate : e.g. Age POP. PK

How to predict exposure ? Exposure Covariate : e.g. Age POP. PK POP. PK + 1 concentration

How to predict exposure ? Exposure Covariate : e.g. Age POP. PK POP. PK + 1 concentration POP. PK + 2 concentrations

Problem of highly variable drugs ? Time Concentration 1 st Administration: fixed dose A blood sample at this time

Problem of highly variable drugs ? Large inter-occasion variability Time Concentration 2 nd Administration: same animal, same dose as 1 st A blood sample at this time

How does it work ? j th concentration measured on the i th animal j th sample time of the i th animal A population model

How does it work ? A set of concentrations on THE animal : (t 1, Z 1 ), (t 2, Z 2 ), … Maximize the a posteriori likelihood Minimize

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