RE: WRES AND OUTLIER IDENTIFICATION/EXCLUSION

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] WRES AND OUTLIER IDENTIFICATION/EXCLUSION Date: Tue, 3 Oct 2006 17:38:09 -0400 Nick, You wrote: "I am still not very comfortable about the fractional likelihood method because it assumes a similar fraction of outlier and non-outlier observations in each subject..." The full likelihood approach using an observation-level mixture model (i.e., residual error mixture model) does not make this assumption. The original version without Mats' modification to use $MIX merely estimates the proportion of outlier observations from the total number of observations. With Mats' $MIX code modification, we estimate the proportion of 'subjects with outliers', thus, the mixing proportion in the residual error mixture model is now conditional on the total number of observations in the population of 'subjects with outliers' rather than the total number of observations. There is no constraint that forces the observation-level mixing proportion to be the same within each subject of the 'subjects with outliers' subpopulation. You wrote: "...more importantly (for this thread) it doesn't distinguish in a discrete way between outlier and non-outlier observations." True...but it doesn't mean we couldn't perform some post hoc calculations to classify observations as outlier or non-outlier based on this full likelihood approach. It is analogous to the situation with $MIX and the post hoc calculations that MIXEST performs. If we did not have the MIXEST capabilities built in to NONMEM we would have a harder time with our diagnostic evaluation of subject-level mixture models using the $MIX functionality. Same is true here with the observation-level mixture models. To fully evaluate and advocate this approach would require more work to determine the post-processing calculations that would allow us to classify the observations in the two populations (outliers vs non-outliers) for diagnostic purposes. Note that if we performed these post hoc calculations such that we could classify outliers vs non-outliers at the observation level we would no longer need to use the $MIX code to identify 'subjects with outliers'. The population of 'subjects with outliers' could be determined directly from these post hoc calculations of the observation-level classification of outliers and non-outliers. Kind regards, Ken _______________________________________________________