Optimal designs for a bivariate logistic regression model

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dc.contributor.authorHeise, Mark A.en
dc.contributor.committeechairMyers, Raymond H.en
dc.contributor.committeememberBirch, Jeffrey B.en
dc.contributor.committeememberCarter, Walter Hans Jr.en
dc.contributor.committeememberHinkelmann, Klaus H.en
dc.contributor.committeememberLentner, Marvin M.en
dc.contributor.committeememberReynolds, Marion R. Jr.en
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T21:14:49Zen
dc.date.adate2006-06-07en
dc.date.available2014-03-14T21:14:49Zen
dc.date.issued1993-04-05en
dc.date.rdate2006-06-07en
dc.date.sdate2006-06-07en
dc.description.abstractIn 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.en
dc.description.degreePh. D.en
dc.format.extentvii, 116 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06072006-124147en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06072006-124147/en
dc.identifier.urihttp://hdl.handle.net/10919/38538en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1993.H457.pdfen
dc.relation.isformatofOCLC# 28528712en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1993.H457en
dc.subject.lcshDrug testingen
dc.subject.lcshLogistic distributionen
dc.subject.lcshRegression analysisen
dc.titleOptimal designs for a bivariate logistic regression modelen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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