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Re: $PRIOR with normal for OMEGA?

From: Jakob Ribbing <jakob.ribbing>
Date: Fri, 11 Nov 2016 08:59:22 +0100

Hi Mark,

Indeed there is: As an alternative to NWPRI, there is the TNPRI =
subroutine that you can use with $PRIOR (frequentist prior).
This functionality is tripple normal, with regards to thetas, omegas and =
I will describe this more in detail than Mark would need (hopefully for =
the benefit of others).

I used to think that TNPRI was an appealing alternative when the =
standard error of population parmeters were all modest. The =
implementation appears to be appealing at a first glance (less error =
prone): Simply plug in the MSFO file from a previous run (generating the =
prior), as a prior representing the covariance matrix from that previous =
In addition, if from that previous run one has reported SEs based on the =
covariance matrix, it may be appealing to use the same distribution when =
simulating with uncertainty in population parameters (what I call =
simulation mode, below), or as a prior in the next analysis with a new =
analysis data set (what I call estimation mode, below).
However, over the years I have been using it less and less due to =
various limitations and “features”.
I am not sure if Marks question was with regards to estimation with =
support of a prior (estimation mode), or simulation with uncertainty in =
population parameters based on a prior distribution (simulation mode), =
but separate the list of bugs/features/limitations we have come across, =
Some of these features are documented, whereas others I believe are not.

In estimation mode (using TNPRI) there are only a few limitations that =
comes to my mind:
Any thetas that are fixed must appear as the last thetas in your model =
(already when generating the prior)
When generating the prior, do not use the UNCONDITIONAL option for the =
covariance step. Even in cases where the estimation is successful (so =
that the UNCONDITIONAL option is not needed), the subsequent estimation =
with TNPRI will fail (If I recall correctly, it will run forever).
If you use PsN: TNPRI is not supported by all programs, in particular, =
you can not use scm. Some may raise their eyebrows, thinking that the =
prior does not allow testing for (new) covariates, so I will adress that =
comment right away. With a new patient population at hand, you may want =
to use scm to test whether there is a significant difference in any of =
the population parameters, as compared to the prior (prior not including =
the new patient population).

In simulation mode (using TNPRI) there are additional limitations that I =
would tend to call bugs, and I will only mention a few:
From the TABLE output you can use IPRED (and the distribution of =
population parameters), but other PRED defined variables can not be =
trusted, including PRED itself: so any clever calculations you may do in =
your control stream (e.g. change from baseline): Do not use it! The =
output may have been generated based on the initial estimates (i.e. =
prior mode, despite TRUE=PRIOR), rather than based on the simulations =
that include uncertainty in population parameters
Limitations on which parameters needs to be fixed is even greater. If I =
remember correctly, the whole model must be re-formulated in case you =
have any terminal thetas: SIGMAs and OMEGAs must then also be fixed (to =
1), and magnitudes estimated as fixed effects (representing e.g. =
standard error of IIV, or the covariance) - these additional thetas must =
then also appear before the fixed thetas. But this is when generating =
the prior (in estimation mode, before the subsequent simulation). =
Possibly, when using the prior in simulation mode, then all previously =
fixed thetas must be unfixed again.
When generating the prior, do not use the UNCONDITIONAL option for the =
covariance step. Even in cases where the estimation is successful (so =
that the UNCONDITIONAL option is not needed), the subsequent simulation =
step will fail (If I recall correctly, it will run forever).

At Pharmetheus, we have not used TNPRI widely and tend to use it less =
and less (favouring NWPRI), and we have never had the time to fully =
characterise these bug/features: as soon as we have concluded it works =
for the task at hand, we leave it without further exploring situations =
where TNPRI may provide an unexpected/erroneous output.
Consequently, you may find my bug/feature description above a bit =
unclear. I do not know exactly what situations trigger these bugs, and I =
could list additional vague descriptions of bugs/features we have come =
across, if I look back into previous projects. But I think if I do that =
it would raise more questions than it answers...
However, this discussion is mainly on simulations, and maybe missess out =
entirely on Marks question? Hopefully, someone will find it useful, =

Finally, back more towards Marks question, if SE is large in the sense =
that the normal (uncertainty) distribution would go outside the =
boundaries (e.g. OMEGA<0), for any population parameter (fixed and =
random), then there is functionality to handle this.
I have never used TNPRI with any large SE:s, but Mats Karlsson once =
mentioned to me that the functionality does not really handle this =
situation the way you would expect: the tail of the distribution that =
goes outside the boundary will be moved to the other end of the =
Obviously, this is not what you want in case that tail constitutes a =
large fraction, but if it is only a question of 1 out of 10 000 sample, =
this may be harmless (in most cases).

Maybe someone can complement with a fuller description on the =
limitations with TNPRI than what I could provide?
Otherwise, I leave you with the following short summary, for when how to =
use TNPRI:
In generating the prior
try to avoid fixing any theta (e.g. do not use a fixed theta to =
represent allometric constants), and if the purpose of TNPRI is =
simulation try to avoid fixing any omega as well
Do not use UNCONDITIONAL in the covariance step
In estimation with support of the TNPRI prior
Be aware you can not use PsN scm, for covariate selection (NWPRI works =
fine with the new nonmem notation THETAP, etc. But you need to be aware =
of the issues of testing covariates with suport of a prior that did not =
include that covariate)
In simulation using TNPRI
From the TABLE output, you may use IPRED (and other variables that are =
not simulated, like ID, trial-replicate nr, time and dose). THETAS, =
OMEGAS and SIGMAS can be used to check the distribution across replicate =
simulations, but pred-defined variables should not be used for anything!

It used to be quite hairy and error prone to manually set up a =
complicated nonmem control stream for using the NWPRI.
However, if you can use automatic functionality for adding the NWPRI =
distribution in the control stream and just check it has been =
implemented correctly, this is not a big hurdle.
For example, PsN has such a functionality as an option to the =
“update_inits” program.
In addition, the new nonmem notation makes it easier for others to =
understand the control stream (THETAP, etc).
Therefore, in most cases where I need to use a (frequentist) prior, =
NWPRI is currently my first option.
(But I leave you with the cheery reservation that I do not mention much =
around limitations/features with NWPRI, since that is clearly out of =
scope for the topic in this tread :>)

Best regards


Jakob Ribbing, Ph.D.

Senior Consultant, Pharmetheus AB

Cell/Mobile: +46 (0)70 514 33 77


Phone, Office: +46 (0)18 513 328

Uppsala Science Park, Dag Hammarskjölds väg 52B

SE-752 37 Uppsala, Sweden

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On 11 Nov 2016, at 04:57, Mark Sale <msale

> Is it possible to use a normal prior for OMEGA? The default is inverse =
Wishart, but I'd be interested in using Normal (insuring that it is =
positive definite) Any ideas?
> thanks
> Mark Sale M.D.
> Vice President, Modeling and Simulation
> Nuventra Pharma Sciences, Inc.
> 2525 Meridian Parkway, Suite 280
> Durham, NC 27713
> Phone (919)-973-0383
> msale
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Received on Fri Nov 11 2016 - 02:59:22 EST

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