RE: Fwd: Should we generate VPCs with or without uncertainty?
Hi Devin and Matts,
Of interest, we had similar internal discussion within our department about
this topic quite recently.
I would agree with Devin that it is preferable to include parameters
uncertainty in a VPC, especially if they are used for relevant decision making.
It may result on large CI around your 5th, median and 95th percentiles, however
it means that you likely have limited information to estimate some of the
variability terms. Don’t forget that any “standard VPC” still provides some
uncertainty around your percentiles based on random effects and sample size.
There are several ways to embed params uncertainty, I found quite useful to use
the covariance-matrix (from NM) to embed it in a simulation script – it is
quite straightforward to do that in R with some coding effort (I think Pirana
has R code for that as well), but I’m sure it can be easily replicated with
different tools available.
I guess it would be interesting to see how pharmacometricians would derive the
parameters uncertainty: i.e, covariance matrix vs bootstrap or other means. I
recently saw an elegant and efficient solution of bootstrap VPC done from a
colleague of mine.
Cheers
Stefano
Stefano Zamuner PhD
Senior Director Clinical Pharmacology
GSK
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Devin Pastoor
Sent: 08 June 2015 17:30
To: Matts Kågedal; [email protected]
Subject: Re: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?
Matts,
The way I see the CI's around the point estimates provided in the VPC can help
provide a useful indication of model robustness, especially in regards to the
impact of random effects components, in that portion of your model. Especially
for heterogeneous data (or even all rich data for that matter) there are a
number of binning strategies that can be used, which can impact the
aforementioned intervals.
At the end of the day, we must use our judgement for how the model is being
used to support decisions, and whether information regarding uncertainty can
provide additional support towards the overall evaluation of the key questions
you are trying to address. Eg, if you are dealing with a narrow therapeutic
index drug the value of having a 'feel' for the robustness of the ability of
your model to describe the tails may be valuable information, even as a
qualitative indication of model robustness. On the other hand, if you are
trying to make a decision regarding dose adjustment between different
populations and are looking to normalize large differences, as well as are
constrained to certain oral dosage options, uncertainty in the point estimates
will likely provide very little support to an argument one way or the other.
Finally, in my opinion, inclusion/exclusion also relies on what the plot is
trying to communicate. Are you trying to personally evaluate model adequacy,
sure, but if using to convey to non- modelers/quantitative people that your
model describes the data - include a visualization of uncertainty at your own
peril :-)
So, for better or worse, I would say - it depends, though I would be highly
concerned if major decisions rode on inclusion/exclusion of parameter
uncertainty, in most cases.
Devin Pastoor
Center for Translational Medicine
University of Maryland, Baltimore
On Mon, Jun 8, 2015 at 11:57 AM Matts Kågedal
<[email protected]<mailto:[email protected]>> wrote:
Hi all,
Creation of VPCs is a way to assess if simulated data generated by the model is
compatible with observed data.
VPCs are usually based on parameter point estimates of the model. Sometimes
parameter uncertainty is also accounted for in the generation of VPCs (PPCs)
where each simulated replicate of the data set is based on a new set of
parameter values representing the uncertainty of the estimates (e.g. based on a
bootstrap).
I wonder if inclusion of uncertainty in this way is really appropriate or if it
just makes the confidence intervals wider and hence easier to qualify the
model. Is it possible based on such an approach, that a model might look good,
when in fact no likely combination of parameter values (based on parameter
uncertainty) would generate data that are compatible with the observations?
To illustrate my question:
I could generate 100 sets of parameters reflecting parameter uncertainty (e.g.
from a bootstrap). Based on each set of parameters I could then generate a
separate VPC (e.g. showing median, 5 and 95% percentile) to see if any of the
parameter sets are compatible with data. I would then have 100 VPCs, each based
on a separate set of parameter values reflecting the parameter correlations and
uncertainty.
If the VPC based on point estimates looks bad, I would (generally) expect that
the other VPCs would be worse (they all have lower likelihood), so that we have
101 VPCs that does not look good. Some might over predict and some
underpredict, some might describe parts of the relation better than the VPC
based on the point estimates.
By putting the VPCs together from all parameter vectors, the CI becomes wider,
and perhaps now includes the observed data. So based on a set of 100 parameter
vectors which individually are not compatible with the observed data I have now
generated a VPC (PPC) where the confidence interval actually includes the
observed metric (e.g median). It seems to me that based on such an approach it
is possible that a model might look good, when in fact no likely individual set
of parameter values would generate data that are compatible with the
observations.
Simulation based on parameter uncertainty is useful when we want to make
inference, but I am unsure of its use for model qualification. In any case it
is confusing that we some times simulate based on point estimates and sometimes
based on parameter uncertainty without any particular rationale as far as I
understand.
Would be interested if someone could shed some light on the inclusion of
uncertainty in simulations for model qualification (VPCs).
Best regards,
Matts Kagedal
Pharmacometrician, Genentech
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