RE: Re: FO vs FOCE vs LAPLACIAN

From: "Kowalski, Ken" <Ken.Kowalski@pfizer.com> Subject: RE: [NMusers] Re: FO vs FOCE vs LAPLACIAN Date: Fri, 18 Jul 2003 08:38:12 -0400 Nick, I know we're rehashing old ground...but I can't resist. Too often the value of $COV is equated solely with getting SEs and Wald-based CIs which we know often don't have the right coverage probabilites. This to me is not the real value of the $COV. When the $COV fails, the hessian (R-matrix) may be singular and/or non-positive semi-definite indicating that the estimates may not have converged to a global optimum and thus they may not be (approximate) maximum likelihood estimates. That being said, I agree with you that this does not mean the estimates aren't any good. However, I do think it means we should proceed cautiously because they might not be good (particularly for extrapolation). In this situation you have previously advocated bootstrapping to assess the stability and predictive performance of the model. I think this a good course of action and a cautious way to proceed. Many who do not place any value in the $COV argue that they often obtain reasonable estimates even when the $COV fails. I argue that they are making use of prior information to make that assessment. If so, I would much rather be more explicit in using that prior information via fixing parameters, fitting a penalized likelihood, or using a fully Bayesian estimation procedure to remove the instability in the model fit. The real value of the $COV is as a diagnostic to assess instability. Of course, a successful $COV does not guarantee that the model is stable nor does it guarantee that the estimates have converged to a global optimum. It is merely a diagnostic to assess stablity and provides some indication as to when we should proceed cautiously. You may think I am jumping through a lot more hoops needlessly to obtain stable models but to me it is no more work than bootstrapping every model with a failed $COV in the development process. I realize that we are going to have to agree to disagree...just don't take $COV away from NONMEM VI as I'm willing to pay for those extra electrons. Ken