Optimal Experimental Designs for the Poisson Regression Model in Toxicity Studies

Optimal experimental designs for generalized linear models have received increasing attention in recent years. Yet, most of the current research focuses on binary data models especially the one-variable first-order logistic regression model. This research extends this topic to count data models. The primary goal of this research is to develop efficient and robust experimental designs for the Poisson regression model in toxicity studies. D-optimal designs for both the one-toxicant second-order model and the two-toxicant interaction model are developed and their dependence upon the model parameters is investigated. Application of the D-optimal designs is very limited due to the fact that these optimal designs, in terms of ED levels, depend upon the unknown parameters. Thus, some practical designs like equally spaced designs and conditional D-optimal designs, which, in terms of ED levels, are independent of the parameters, are studied. It turns out that these practical designs are quite efficient when the design space is restricted. Designs found in terms of ED levels like D-optimal designs are not robust to parameters misspecification. To deal with this problem, sequential designs are proposed for Poisson regression models. Both fully sequential designs and two-stage designs are studied and they are found to be efficient and robust to parameter misspecification. For experiments that involve two or more toxicants, restrictions on the survival proportion lead to restricted design regions dependent on the unknown parameters. It is found that sequential designs perform very well under such restrictions. In most of this research, the log link is assumed to be the true link function for the model. However, in some applications, more than one link functions fit the data very well. To help identify the link function that generates the data, experimental designs for discrimination between two competing link functions are investigated. T-optimal designs for discrimination between the log link and other link functions such as the square root link and the identity link are developed. To relax the dependence of T-optimal designs on the model truth, sequential designs are studied, which are found to converge to T-optimal designs for large experiments.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2002

Author dc:creator

• Wang, Yanping

Chairs dc:contributor.committeechair

• Smith, Eric P.
• Ye, Keying

Committee members dc:contributor.committeemember

• Myers, Raymond H.
• Anderson-Cook, Christine M.
• Birch, Jeffrey B.

• Poisson Regression Model
• Design Optimality
• Experimental Design

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-07282002-150028

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28426