RE: WRES AND OUTLIER IDENTIFICATION/EXCLUSION

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] WRES AND OUTLIER IDENTIFICATION/EXCLUSION Date: Thu, 28 Sep 2006 17:08:59 -0400 Mats, We appear to be in good agreement on all points. Thank you for your kind words regarding (4) and info on Dr. Sadray's (et al.) paper...I will certainly take a look at it. I just have a follow up with regards to your responses to (2). 2) Certainly work needs to be done to evaluate whether this approach indeed has merit. I agree there is no reason necessarily to believe outliers are normal, however, we most likely will lack suitable power to assess the distribution of these outlying data. There is precedence to consider a mixture model of normal distributions, referred to in the statistical literature as a contaminated normal distribution where Y is distributed as (1-p)N(mu,sigma) + (p)N(mu,k(sigma)) where p represents the fraction of outliers and k is the scale parameter for the increased variation in the outliers (see Barnett and Lewis, Outliers in Statistical Data, Wiley, 1978, pp 31-33, 127-130). We propose a two-stage approach to this contanimated normal distribution by first estimating p by use of a prespecified outlier criteria and fixing this through the use of the FLAG variable. In the second stage we estimate k which is the ratio of sigma2 to sigma1. The outlier criteria, which would ideally be specified in the analysis plan before starting the model development, might be something like "flag all data points as potential outliers for further evaluation where abs(IWRES)>5" (perhaps a reasonable criteria with dense data). Of course, we could look at a full likelihood mixture model approach were p and k are simultaneously estimated. There are other contaminated normal mixture models that allow for asymmetry (a shift in mu as well as a scale increase in sigma) and of course mixtures of different distributions between non-outliers and outliers. Whether we have enough power to discern between various contaminated distributions and how well they may perform in the context of PK/PD is certainly an area that could benefit from some research. Kind regards, Ken