Preliminary Test Estimation Procedures in Nonlinear Regression Models with Toxicological Application

• Activity Number: 177
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Changwon Lim*+ and Pranab Kumar Sen and Shyamal D. Peddada
• Companies: National Institute of Environmental Health Sciences and The University of North Carolina at Chapel Hill and National Institute of Environmental Health Sciences
• Keywords: Asymptotic normality ; Dose-response study ; Heteroscedasticity ; Hill model ; M-estimation procedure ; Nonlinear regression model

Abstract

Often toxicologists are interested in investigating the dose-response relationship when animals are exposed to varying doses of a chemical. Usually a nonlinear regression model such as a Hill model is used to describe the relationship. Depending upon various factors, including the bioassay, the data may be homoscedastic or heteroscedastic, which, in practice, is not generally known a priori. Since the performance of the method of analysis relies on the structure of the error variance of the data, in this article a simple preliminary test estimation (PTE) is introduced to select an appropriate methodology. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of PTE are investigated and the proposed methodology is illustrated using a toxicology data.