logistic regression: NONMEM LAPLACIAN vs. Gaussian quadrature

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

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

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).

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

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

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 _______________________________________________________