A Nonparametric Analogue to POSTHOC Estimates for Exploratory Data Analysis
Robert H. Leary and Jason Chittenden
Pharsight Corporation
The use of FO or FOCE posthoc eta values for exploratory data analysis of possible covariate relationships and correlations (e.g., regressing post hoc estimates of a clearance or volume of distribution against weight or against other posthocs) is a commonly used approach. However, as shown in [1], shrinkage effects may hide or distort an actual dependence or correlation, possibly rendering such analyses ineffective or even misleading. Recently NONMEM VI has added a relatively simple nonparametric capability in which the discrete nonparametric maximum likelihood (ML) distribution is approximated by a discrete distribution with support points fixed at the posthoc estimates from a preliminary parametric FO or FOCE analysis, with likelihood optimization only over the associated probabilities on the support points. Due to shrinkage, the supports may be badly placed relative to the supports in a nonparametric ML distribution that has also been optimized with respect to support point positions. Here we investigate the use of the mean of the individual nonparametric posterior distributions as a nonparametric analogue to parametric posthocs in exploratory data analysis. Examples are shown based on simple simulations to illustrate the resiliency of this mean to shrinkage effects, as well as the advantage of using the fully optimized nonparametric distribution.
Reference:
[1] R. M. Savic and M. O. Karlsson, Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics and Estimation: Problems and Solutions, PAGE 2007, abstract 1087.
