A three-parameter logistic regression model. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Yu, Xiaoli; Li, Shaoting; Chen, Jiahua
• Is Part Of: Statistical theory and related fields. Volume 5:Issue 3(2021)
• Page Start: 265
• Page End: 274
• Publication Date: 2021-07-03
• Subjects: dose–response experiment -- effective dose level -- optimal design -- sequential ED-design -- up-and-down design -- vertex direction method; Primary: 62K05 -- Secondary: 62L05; Statistics -- Periodicals; Statistics; Periodicals; Electronic journals; 001.422
• DOI: 10.1080/24754269.2020.1796098
• Languages: English
• ISSNs: 2475-4269

Abstract

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.