From Thu Mar 13 23:26:33 1997
Subject: Any tools for Bayesian estimation?

I attempt to estimate individual eta's from individual measurements using pre-determined theta's, omega's and epsilon's which are obtained by NONMEM methods from a set of data. Does anyone know any application programs for Bayesian estimation that covers the following requirement:

1. Easy modeling:
Feasiblility which allows to use any models described using subroutins of ADVAN and TRANS in the NONMEM.

2. Error modeling:
Both relative and absolute errors(epsilon's) can be modeled simultaneously.

I think it is difficult to understand what two-error-model means, because an estimate for an individual error is only one value that is the difference between observed and estimated concentrations. However, when one estimates using observed values in a wide rage, relative error is suitable for large values and absolute error is for small values near to lower quantitation limit. So, the errors in Bayesian estimation should be evaluate using relative or absolute error models which give preferable likelyhood.

3. Executable on PC with Windows95
Any programs or macros executable directly on PC, using spreadsheet for Windows, or with WinNonlin is preferable.

Many thanks,

Masaki Hiraoka
Kanagawa Laboratories,
Bristol-Myers Squibb K.K.


From alison Mon Mar 17 09:43:07 1997
Subject: Bayesian estimates

Recently, Masaki Hiraoka asked this question:

"I attempt to estimate individual eta's from individual measurements using pre-determined theta's, omega's and epsilon's which are obtained by NONMEM methods from a set of data. Does anyone know any application programs for Bayesian estimation ..."

I told him that, with the POSTHOC option of the $ESTIMATION record, NONMEM can obtain individual etas via Bayesian method.

He then asked me:

"Can NONMEM calculate etas for the subject, when the thetas, omegas and epsilons are fixed to the previously obtained values?"

This is the answer that I sent him, which may be of interest to other people.

Alison Boeckmann


Yes. Use the MAXEVALS=0 option of $ESTIM. E.g.,

THETA ... any values
$OMEGA ...
$SIGMA ...

NONMEM will obtain individual estimates of etas based on the given values of theta, omega, sigma. Because of MAXEVALS=0, it will not try to change these values from their initial estimates. Note that these values do not have to be from an earlier successful Estimation Step, and do not have to be a miniumum of the objective function for any data set. (This is unlike the Covariance step, which can only be run after a minimum has been found.) For example, they can be values obtained from the literature.

A convenient way to provide the initial estimates is from a Model Specification file written by an earlier run. E.g.,

$MSFI msfpop

The file msfpop must have been obtained earlier, e.g.,

$ESTIM MSFO=msfpop

This earlier run did not have MAXEVALS=0, hence the estimation step was implemented.


From Wed Mar 26 19:49:48 1997
Subject: Any tools for Bayesian estimation? (fwd)

Regarding Bayesian methods for dos-individualisation

Most Bayesian methods offer easy modelling. However it is important to note that I know of none that allow the flexibility offered by NONMEM in terms of model definition. I have some familiarity with ABBOTTBASE, USC-PACK, and SeBA programs and none of these allow complex model description (at least not more complex than 2-3 cpt linear models or 1 cpt nonlinear models).

Most Bayesian programs that I have used do not allow specific modelling of residual error terms for an individual. Some methods, that would allow this, have been described, eg. Wakefield JPB 1996;24:103-31. However this technique does not appear to be commercially available yet.

The SeBA programs (described by Duffull, Cancer Chemother Pharmacol 1997;39:317-26 , Duffull, BJCP 1997;43:125-135 and Duffull, Proc Aust Soc Clin Exp Phamracol Toxicol 1996;3:58) may offer a potential advantage over other Bayesian programs in that they allow within patient variability to be modelled as changes in the structural PK parameters. The SeBA programs use a Sequential Bayesian Algorithm that analyse each set of concentration-time data for each dose, thereby continuously updating the prior model. This allows the prior model to `grow' to become more like the patient. It allows description of changes that may occur in a patients PK parameter values over a course of therapy (sometimes referred to as interoccasion variability) in the absence of changes in the patient's covariates. This might be expected to be beneficial for patients who are acutely ill at the beginning of treatment and whose condition is expected to improve due to the intervention (eg gentamicin).

Generally the error term used in a Bayesian program that uses MAP is assay error, only. With few exceptions the source of error from the assay significantly outways errors from other sources (eg model misspecification etc). However users can also define the variance of the residual error in the MAP algorithm as the proportional error component given by NONMEM (eg ABBOTTBASE). USCPACK allows the user to describe the variance of the residual error using a quadratic function. The SeBA programs can use proportional or proportional and additive as desired.

All of the programs mentioned are executable on a PC, most are DOS based rather than Windows.

I hope this has been of some use.

Steve Duffull
Dept of Clinical Pharmacology
Christchurch Hospital
Private Bag 4710, CHCH
Ph +64 3 364 0900
Fax +64 3 364 0902