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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
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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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)