A three-parameter logistic regression model

Abstract

Dose–response experiments and data analyses are often carried out according to an optimal design under a model assumption. A two-parameter logistic model is often used because of its nice mathematical properties and plausible stochastic response mechanisms. There is an extensive literature on its optimal designs and data analysis strategies. However, a model is at best a good approximation in a real-world application, and researchers must be aware of the risk of model mis-specification. In this paper, we investigate the effectiveness of the sequential ED-design, the D-optimal design, and the up-and-down design under the three-parameter logistic regression model, and we develop a numerical method for the parameter estimation. Simulations show that the combination of the proposed model and the data analysis strategy performs well. When the logistic model is correct, this more complex model has hardly any efficiency loss. The three-parameter logistic model works better than the two-parameter logistic model in the presence of model mis-specification.

Keywords:

• dose–response experiment
• effective dose level
• optimal design
• sequential ED-design
• up-and-down design
• vertex direction method

MSC 2010:

• Primary: 62K05
• Secondary: 62L05

Acknowledgments

The authors gratefully acknowledge the fundings from the National Natural Science foundation of China, 11871419 and the Natural Science and Engineering Research Council of Canada.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors gratefully acknowledge the fundings from the National Natural Science foundation of China [Grant Number 11871419] and the Natural Science and Engineering Research Council of Canada.

Notes on contributors

Xiaoli Yu

Dr. Xiaoli Yu is currently self-employed.

Shaoting Li

Dr. Shaoting Li is an associate professor at the School of Statistics, Dongbei University of Finance and Economics.

Jiahua Chen

Jiahua Chen is Canada Research Chair, tier I at the Department of Statistics, University of British Columbia.