RE: Confidence intervals of PsN bootstrap output
Hi Jakob,
I agree that in the well-defined cases that reparameterization will not
matter since maximum likelihood is invariant under certain types of
transformation - your bootstrap distribution would be the same. For the
marginal dataset cases (for any dataset bootstrap or otherwise)
transformation will help convergence and COV step estimation by helping
with boundary problems and reducing intrinsic nonlinearity. For
pathological cases such as those in which a few individuals contain
information to estimate key parameters or when there are certain types of
outlying individuals, one should consider the accuracy of the bootstrap
estimate. Just my opinion.
Best Regards,
Matt
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Ribbing, Jakob
Sent: Monday, July 11, 2011 7:43 PM
To: nmusers
Cc: Matt Hutmacher
Subject: RE: [NMusers] Confidence intervals of PsN bootstrap output
Hi Matt,
OK, I can certainly see that transformations will be helpful in
bootstrapping; for those persons that throw away samples with unsuccessful
termination or cov step. They would otherwise discard all bootstrap
estimates that indicate Emax is close to zero. Since I most often use all
bootstrap samples that terminate at a minimum I guess in practice I would
virtually have the same distribution of Emax, regardless of transformation
or not?
I fully agree transformations are useful to get convergence and successful
covstep on the original dataset (and I tend to keep the same transformation
when bootstrapping, but only for simplicity). However, I sometimes use the
bootstrap results to which parameters should be transformed in the first
place. From what I have seen, bootstrapping the transformed model again has
never changed the (non-parametric bootstrap) distribution when boundaries
were the same (e.g. both models bound to positive values of Emax).
Cheers
Jakob
-----Original Message-----
From: Matt Hutmacher [mailto:[email protected]]
Sent: 11 July 2011 17:39
To: Ribbing, Jakob; 'nmusers'
Subject: RE: [NMusers] Confidence intervals of PsN bootstrap output
Hi Jakob,
"The 15% bootstrap samples where data suggest a negative drug effect would
in one case terminate at the zero boundary, in the other case it would
terminate (often unsuccessfully) at highly negative values for log Emax"...
I have seen that transformation can make the likelihood surface more stable.
In my experience, when runs terminate using ordinary Emax parameterization
with 0 lower bounds (note that NONMEM is using a transformation behind the
scenes to avoid constrained optimization), you can avoid termination and
even get the $COV to run with different parameterizations. The estimate
might be quite negative as you suggest, but I have seen it recovered. Also,
I have seen termination avoided and COV achieved with Emax=EXP(THETA(X)) and
EC50=EXP(THETA(Y)) when EC50 and EMAX becomes large. I have seen variance
components that can be estimated in this way but not with traditional $OMEGA
implementation.
Best,
matt