Optimal designs for a bivariate logistic regression model

In drug-testing experiments the primary responses of interest are efficacy and toxicity. These can be modeled as a bivariate quantal response using the Gumbel model for bivariate logistic regression. D-optimal and Q-optimal experimental designs are developed for this model The Q-optimal design minimizes the average asymptotic prediction variance of p(l,O;d), the probability of efficacy without toxicity at dose d, over a desired range of doses. In addition, a new optimality criterion, T -optimality, is developed which minimizes the asymptotic variance of the estimate of the therapeutic index. Most experimenters will be less familiar with the Gumbel bivariate logistic regression model than with the univariate logistic regression models which comprise its marginals. Therefore, the optimal designs based on the Gumbel model are evaluated based on univariate logistic regression D-efficiencies; conversely, designs derived from the univariate logistic regression model are evaluated with respect to the Gumbel optimality criteria. Further practical considerations motivate an exploration of designs providing a maximum compromise between the three Gumbel-based criteria D, Q and T. Finally, 5-point designs which can be generated by fitted equations are proposed as a practical option for experimental use.

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

1993

Author dc:creator

• Heise, Mark A.

Chair dc:contributor.committeechair

• Myers, Raymond H.

Committee members dc:contributor.committeemember

• Birch, Jeffrey B.
• Carter, Walter Hans Jr.
• Hinkelmann, Klaus H.
• Lentner, Marvin M.
• Reynolds, Marion R. Jr.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en

Dc Identifier Other

etd-06072006-124147

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38538