On Estimation in Non-linear Mixed Models with Applications to Pharmacokinetics

• Activity Number: 215
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 12:00 PM to 1:50 PM
• Sponsor: Biopharmaceutical Section*
• Author(s): Max Petzold*+
• Affiliation(s): Göteborg University
• Keywords: Mixed models ; Prediction ; Small sample

Abstract

Estimators of unknown parameters in a model are often dependent of each other. Replacing a given value with an unknown parameter P will then influence the properties of the other estimators. Before deciding whether making an effort to derive a theoretically founded value or estimating P from the data, the researcher has to consider the needs for the study. One aspect is the variance of the estimators, which can be considerably smaller when P is given. Another aspect is the Mean-Squared-Error-of-Prediction (MSEP) measuring the combined effect of the resulting variance and bias for a given but biased assignment.

This kind of consideration can be relevant for a power parameter p in regression. Here, a mixed model setting suitable for dose/concentration studies is examined. The relative difference in variance of the estimators--i.e., given p or not--is found to be dependent of the level of p. For example, when predicting the mean function, this implies that a relative bias of the assignment will be unequally well-compensated in terms of MSEP for different levels of p. Finally, the results are compared with a non-parametric approach and discussed in general.