Minimal Plus One Point Designs for Testing Lack of Fit for Some Sigmoid Curve Models

• Activity Number: 405
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Ying Su*+ and Damaraju Raghavarao
• Companies: Merck and Temple University
• Keywords: D-optimality ; Goodness-of-fit test ; Sigmoid curve ; Logistic function ; Probit function ; Gompertz model

Abstract

Sigmoid curves are widely used nonlinear models in biological sciences and biopharmaceutical research. D-optimal designs for nonlinear models are often minimally supported, i.e., the number of support points is equal to the number of parameters in the model. They have been frequently criticized for their inability to test for lack of fit. We construct alternative designs to address this issue for some commonly used sigmoid curves, including logistic, probit and Gompertz models with two, three or four parameters. For each model, we compare five non-minimally-supported designs in terms of their efficiency, and propose designs that are both statistically efficient and practically convenient for practitioners.