Optimal block designs for experiments with responses drawn from a Poisson distribution

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dc.contributor.author Bush, S en
dc.contributor.author Ruggiero, Katya en
dc.date.accessioned 2018-10-04T21:50:25Z en
dc.date.issued 2016-01-05 en
dc.identifier.citation Arxiv (1601.00477) 04 Jan 2016. 20 pages. en
dc.identifier.uri http://hdl.handle.net/2292/38928 en
dc.description.abstract Optimal block designs for additive models achieve their efficiency by dividing experimental units among relatively homogenous blocks and allocating treatments equally to blocks. Responses in many modern experiments, however, are drawn from distributions such as the one- and two-parameter exponential families, e.g., RNA sequence counts from a negative binomial distribution. These violate additivity. Yet, designs generated by assuming additivity continue to be used, because better approaches are not available, and because the issues are not widely recognised. We solve this problem for single-factor experiments in which treatments, taking categorical values only, are arranged in blocks and responses drawn from a Poisson distribution. We derive expressions for two objective functions, based on DA- and C-optimality, with efficient estimation of linear contrasts of the fixed effects parameters in a Poisson generalised linear mixed model (GLMM) being the objective. These objective functions are shown to be computational effcient, requiring no matrix inversion. Using simulated annealing to generate Poisson GLMM-based locally optimal designs, we show that the replication numbers of treatments in these designs are inversely proportional to the relative magnitudes of the treatments' expected counts. Importantly, for non-negligible treatment effect sizes, Poisson GLMM-based optimal designs may be substantially more efficient than their classically optimal counterparts. en
dc.relation.ispartof Arxiv en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html en
dc.title Optimal block designs for experiments with responses drawn from a Poisson distribution en
dc.type Report en
dc.rights.holder Copyright: The authors en
pubs.author-url https://arxiv.org/abs/1601.00477 en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Working Paper en
pubs.elements-id 686954 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.number 1601.00477 en
pubs.record-created-at-source-date 2017-10-09 en


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