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RE: Confidence intervals of PsN bootstrap output

From: Ribbing, Jakob <Jakob.Ribbing>
Date: Mon, 11 Jul 2011 13:23:34 +0100

Resending and apologizing for any duplicate messages!

-----Original Message-----
From: Ribbing, Jakob
Sent: 11 July 2011 10:13
To: nmusers
Subject: RE: [NMusers] Confidence intervals of PsN bootstrap output

All,

This first part is more to clarify and I do not believe this is in
disagreement with what has been said before. The last paragraph is a
question.

The two examples I mentioned regarding boundary conditions are regarding
variance parameters. The second of these, however, is with regards to a
boundary at eta-correlation of one, which is a must rather than just an
irritating NONMEM feature.

I used these examples because they were less controversial and it is
difficult to come up with general statements that apply to all cases.
However, as a third example for a fixed-effects parameter: Imagine a
covariate acting in a linear fashion on a structural parameter that is
bound to be non-negative (e.g. a rate constant, volume, clearance, ED50,
etc). Imagine boundaries on the covariate parameter have been set to
avoid negative values for the structural-model parameter (on the
individual level). For this scenario if a substantial fraction of the
bootstrapped covariate-parameter values end up at one of the boundaries,
one may have to consider two options:
a) Decide that a linear covariate model is inappropriate (at least for
the goal of extrapolating to the whole population with more extreme
covariate values) and change the model into using a different functional
form
b) Dismiss this as random chance, due to small sample/limited
information and a (covariate) slope which "truly" is not far from one of
the boundaries. If this is the case, deleting the bootstrap estimates at
boundary would bias the distribution in an undesirable manner. For that
case the boundary condition is not due to local minimum and we would not
want to discard bootstrap samples at boundary). (Nick's example is of a
different kind, where it is either a local minimum or else not reaching
a minimum at all)

A related question - I am thinking more in terms of simulations with
parameter uncertainty; not just obtaining CI, which was originally what
this thread was about:
There are sometimes situations where a limited set of (clinical-) trial
data gives reasonable point estimates but with huge parameter
uncertainty (regardless nonmem covmaxtrix or bootstrap with appropriate
stratification). The distribution and CI on these parameters may include
unreasonable values, even though there is no obvious physiological
boundary (unreasonable based on prior knowledge that has not been
incorporated into the analysis, e.g. for a certain mechanism and patient
population Typical-Emax beyond 400% or 10 units - depending on if Emax
is parameterised as relative or absolute change). In these situations, a
simplistic option could be to trim one or both ends with regards to the
Emax distribution and discard these bootstrap samples, especially if
only a few values are unreasonable. Alternatively, before running the
bootstrap, one may set the boundary in the control stream (a boundary
that everyone can agree is unreasonable). One would then keep bootstrap
samples that ends up at this boundary for bootstrap distribution, which
is in a way truncated, but so that bootstrap samples indicating linear
concentration/dose-response maintains almost reasonable Emax and
ED50/EC50 values (but as a spike in the distribution at upper Emax).
Notice that re-parameterising the Emax model would not solve the
underlying issue with unreasonable estimates and reducing to a linear
model may be unsuitable, both based on the original dataset and also for
mechanistic reasons). Could you suggest alternative ways of dealing with
this, for these rather general examples (other than the obvious of
applying an informative prior on Emax)? I would be interested in your
solutions both in terms of the non-parametric bootstrap as well as the
parametric bootstrap (based on the nonmem covmatrix).

Much appreciated

Jakob


-----Original Message-----
From: owner-nmusers
On Behalf Of Nick Holford
Sent: 11 July 2011 06:37
To: nmusers
Subject: Re: [NMusers] Confidence intervals of PsN bootstrap output
Received on Mon Jul 11 2011 - 08:23:34 EDT

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