A New Sigmoid-Shaped Regression Model with Bounded Responses

• Activity Number: 688
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Nancy Flournoy*+ and HaiYing Wang
• Companies: University of Missouri-Columbia and IMS
• Keywords: bioassay ; nonlinear regression ; optimal design ; toxicology

Abstract

We introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model which is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. Because responses often have unknown bounds, our model better reflects the data-generating mechanism. Complications arise because the likelihood is unbounded, and global maximizers are not consistent estimators of unknown parameters. We prove that, with probability approaching one as the sample size goes to infinity, there exists a local solution to the likelihood equation that is consistent at the rate of the square root of the sample size and it is asymptotically normally distributed.

Under this model, we theoretically obtain that an optimal design that minimizes an information based criterion consists at most five design points including the two boundary points of the design space. Additional theoretical results and numerical examples are provided.