RE: $OMEGA blocks and log-likelihood profiling

From: Leonid Gibiansky lgibiansky@emmes.com Subject: RE:[NMusers] $OMEGA blocks and log-likelihood profiling Date: Thu, June 10, 2004 4:29 pm Nick, I do not have an opinion on the subject that you raised: "The hypothesis that successful runs (+/- $COV) are better than all bootstrap runs". However, the question of whether to accept "strongly failed" bootstrap runs (that have parameters defined with zero significant digits or with undefined OF) is interesting to discuss. Can someone offer an example when "strongly failed" NONMEM run was used in any paper or regulatory submission? My guess would be no. I would simplify the model, fix some parameters or do any other possible tricks to get reasonable convergence. I think the criteria for accepting the bootstrap runs should be similar. We cannot accept "strongly failed" runs simply because they have parameters similar to those that converged. They need to be treated as failed, with undefined parameters. The next question is what to do with those. One can try to push them to convergence with several starting points (initial parameters). This would be my choice, but it need to be automated. Another option is to place them at the tails of the distribution: say if 5% of runs "strongly failed" then the most you can count on is to look for the bounds in the 5 to 95% interval (5% set aside for the failed runs). But his might be too strict. The other option (actually, my favorite) is to look on the bootstrap as a useful diagnostics of the problem, not the tool to get confidence intervals with great precision. Then 5% of "strongly failed" runs can be ignored and the rest used for approximate diagnostics, investigation of the parameter distributions, publishing nice papers with bootstrap figures, etc. Have a nice trip to PAGE and Europe ! Leonid