From: Leonid Gibiansky leonidg@metrumrg.com
Subject: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 06:36:08 -0400

On the recent PAGE meeting, Dr. Geert Verbeke gave a very interesting tutorial/review of various estimation
methods as applied to the logistic regression models ( http://www.page-meeting.org/page/page2006/GeertVerbeke.pdf ). 
He mentioned that FO method (MQL in his notation) is always biased for these models;  FOCE method (PQL) is better 
but is reasonably good only if you have a lot of observations per subject; and that the methods based on the
Gaussian quadrature approach to computation of the integrals are much better than both MQL and PQL. He also
mentioned that the methods based on the higher-order Taylor expansions of the integrand (e.g., NONMEM with
LAPLACE option; note that NONMEM LAPLACE is NOT THE SAME as Laplace method that was described in the tutorial)
are much better than FO/FOCE and comparable with the methods based on Gaussian quadratures.

Related question: have anybody compared NONMEM LAPLACE with Gaussian quadrature-based methods for the
logistic regression models that we see in PK-PD modeling? Is it possible to give some recommendations
when it is safe to use NONMEM with LAPLACE option and when one has to try other packages that implement
Gaussian quadrature approach? Any recommendation of those alternative packages (SAS, R/S+)?

Thanks
Leonid 
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From: "Xiao, Alan" alan_xiao@merck.com
Subject: RE: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 07:15:04 -0400

The Conditional Laplace Like approach in NONMEM is fairly comparable with
SAS logistic regression, from my experience.

Alan
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From: "A.J. Rossini" blindglobe@gmail.com
Subject: Re: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 13:57:10 +0200

That would suggest a problem, since generalized linear mixed effects models using logistic links should
generally be "biased" compared with a similar fixed effects or population average (GEE, etc) model.
(bias is in the eye of the beholder , of course -- the point is that when fit on the same models,
they ought to be different).

-- 
best,
-tony

blindglobe@gmail.com
Muttenz, Switzerland.
"Commit early,commit often, and commit in a repository from which we can easily
roll-back your mistakes" (AJR, 4Jan05).
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From: "Ludden, Thomas (MYD)" luddent@iconus.com
Subject: Re: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 09:13:57 -0400

Stuart Beal had explored the use of a quadature method as a refinement step after an initial conditional
estimation analysis.  He referred to this procedure as the Stieltjes Method.  This method is not implemented
in the current NONMEM VI beta and, to avoid any additional delay, this method will not be present in the
initial release of NONMEM VI.  However, an examination of the Fortran code for the Stieltjes Method indicates
that it may be possible, if testing shows that it would be useful, to implement this method in a
later release of NONMEM VI.

Tom Ludden 
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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 09:36:44 -0400

Robert

SAS is an expensive software not available in many universities and small companies; even where SAS is
available, it is usually statisticians, not modelers who know and use it most. So it would be nice to have
a reliable NONMEM procedure to analyze this type of data, or at least know when one can use NONMEM and
when one has to switch to SAS.

Thanks
Leonid
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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature
Date: Mon, 26 Jun 2006 09:37:30 -0400

Thanks to everyone who replied for the helpful references. I think, I was incorrect in interpretation of LAPLACE
option in NONMEM as an indicator for the second-order Taylor expansion of the model ( f(eta) ). In fact, it is
similar to Laplace method described in the tutorial, and hence it place in the estimation methods hierarchy is more clear
( http://www.cognigencorp.com/nonmem/nm/97may202004.html )

Thanks
Leonid 
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