- On 22 Aug 2001 at 12:06:15, "Hans Proost" (J.H.Proost.-at-.farm.rug.nl) sent the message

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The following message was posted to: PharmPK

Dear Colleagues,

I have a question with respect to a Bayesian Two-Stage method for

PK and PKPD analysis. This method has been described in two

excellent papers:

- Mentr=C8 F, Gomeni R. A two=17step iterative algorithm for estimation

in nonlinear mixed=17effect models with an evaluation in population

pharmacokinetics. J Biopharm Stat 1995; 5: 141=17158{PRIVATE }

- Bennett JE, Wakefield JC. A comparison of a Bayesian

population method with two methods as implemented in

commercially available software. J Pharmacokinet Biopharm 1996;

24: 403=17432

In my experience, this method works very well. It is not really

difficult to implement, and Monte Carlo simulations demonstrate its

excellent characteristics with respect to accuracy and precision.

Now towards my question. Usually, PK and PKPD parameters vary

between individuals, and it is the aim of the population analysis to

identify the distribution within the population, usually expressed as

mean and sd (assuming normal or log-normal distribution).

However, in PKPD analysis, some parameters may be assumed to

be similar in all patients, e.g., a dissociation constant of drug-

receptor complex (Kd), or the potency ratio of metabolites or

isomers (e.g. the ratio EC50_metabolite / EC50_parent).

My question is: how can such a parameter be estimated (typical

value and SE or confidence interval) by the Bayesian Two-Stage

approach?

Of course, the most obvious and simple procedure would be to

treat this parameter as a constant, and to calculate the log-

likelihood (or AIC) for some plausible value of that constant. Then

repeat the procedure for a different value of that constant, until the

maximum likelihood is found (or minimum AIC). The confidence

interval could be obtained from the log-likelihood profile.

This is, however, a trial-and-error procedure. Even when performed

automatically, e.g. by a Simplex algorithm, this procedure is not

really efficient. Also, I am not sure that this procedure would

produce an unbiased estimate of the required parameter value and

SE or confidence interval (although this could be checked by

Monte Carlo analysis).

I would appreciate any suggestion on this method, in particular on

more efficient and/or more sound procedures for this problem.

Best regards,

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.-a-.farm.rug.nl - On 23 Aug 2001 at 16:30:11, "Hans Proost" (J.H.Proost.at.farm.rug.nl) sent the message

Back to the Top

The following message was posted to: PharmPK

Dear Colleagues,

I have a question with respect to a Bayesian Two-Stage method for

PK and PKPD analysis. This method has been described in two

excellent papers:

- Mentr=C8 F, Gomeni R. A two=17step iterative algorithm for estimation

in nonlinear mixed=17effect models with an evaluation in population

pharmacokinetics. J Biopharm Stat 1995; 5: 141=17158{PRIVATE }

- Bennett JE, Wakefield JC. A comparison of a Bayesian

population method with two methods as implemented in

commercially available software. J Pharmacokinet Biopharm 1996;

24: 403=17432

In my experience, this method works very well. It is not really

difficult to implement, and Monte Carlo simulations demonstrate its

excellent characteristics with respect to accuracy and precision.

Now towards my question. Usually, PK and PKPD parameters vary

between individuals, and it is the aim of the population analysis to

identify the distribution within the population, usually expressed as

mean and sd (assuming normal or log-normal distribution).

However, in PKPD analysis, some parameters may be assumed to

be similar in all patients, e.g., a dissociation constant of drug-

receptor complex (Kd), or the potency ratio of metabolites or

isomers (e.g. the ratio EC50_metabolite / EC50_parent).

My question is: how can such a parameter be estimated (typical

value and SE or confidence interval) by the Bayesian Two-Stage

approach?

Of course, the most obvious and simple procedure would be to

treat this parameter as a constant, and to calculate the log-

likelihood (or AIC) for some plausible value of that constant. Then

repeat the procedure for a different value of that constant, until the

maximum likelihood is found (or minimum AIC). The confidence

interval could be obtained from the log-likelihood profile.

This is, however, a trial-and-error procedure. Even when performed

automatically, e.g. by a Simplex algorithm, this procedure is not

really efficient. Also, I am not sure that this procedure would

produce an unbiased estimate of the required parameter value and

SE or confidence interval (although this could be checked by

Monte Carlo analysis).

I would appreciate any suggestion on this method, in particular on

more efficient and/or more sound procedures for this problem.

Best regards,

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.at.farm.rug.nl

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