mODa 8Model-Oriented Design and Analysis

Programme and Abstracts

June 4-8, 2007University of Castilla-La Mancha

Almagro, (Spain)

Editors: Mariano Amo-Salas,Raul Martın-Martın,Licesio J. Rodrıguez-Aragon.

Cover Design: Jose Manuel Sanchez-Santos.I.S.B.N.: 978-84-690-6294-4

MODA COMMITTEEA.C. Atkinson, London School of Economics

A. Di Bucchianico?, Eindhoven University of TechnologyV.V. Fedorov?, GlaxoSmithKline

A. Giovagnoli?, University of BolognaP. Hackl, Vienna University of Economics and Business Administration

C.P. Kitsos, Technological Educational Institute of AthensH. Lauter, University of Potsdam

J. Lopez-Fidalgo?, University of Castilla-La ManchaW.G. Muller, University of Linz

A. Pazman, Comenius University BratislavaL. Pronzato, Universite de Nice Sophia Antipolis

R. Schwabe, University of MagdeburgB. Torsney, University of Glasgow

I.N. Vuchkov, University of Chemical Technology & Metallurgy, SofiaH.P. Wynn?, London School of Economics

A.A. Zhigljavsky, University of Cardiff

LOCAL ORGANISING COMMITTEEM. Amo-Salas, University of Castilla-La Mancha

M. Fernandez-Guerrero, University of Castilla-La ManchaS.A. Garcet-Rodrıguez, University of Salamanca

J. Lopez-Fidalgo, University of Castilla-La Mancha (Chair)R. Martın -Martın, University of Castilla-La Mancha

I.M. Ortız-Rodrıguez, University of AlmerıaM.J. Rivas-Lopez, University of Salamanca

L.J. Rodrıguez-Aragon University of Castilla-La ManchaJ.M. Rodrıguez-Dıaz, University of Salamanca

C. Rodrıguez-Torreblanca, University of AlmerıaM.T. Santos-Martın, University of Salamanca

C. Trandafir, University of Valladolid

CONFERENCE SECRETARY

Marıa Jesus Perez

? Organising Committee

TABLE OF CONTENTS

MODA CHARTER 7

CONFERENCE PROGRAMME 11

ABSTRACTS 19

SOCIAL EVENTS 67

AUTHOR INDEX 75

LIST OF PARTICIPANTS 77

Moda Charter mODa8

MODA CHARTER

Preamble

mODa is a series of conferences focused on non-standard design of experiments and therelated analysis of data. The acronym stands for Model-Oriented Data Analysis andOptimum Design. The following guidelines have been issued by the mODa committeein their meeting at Puchberg/Schneeberg and are based on previous versions. It is acommon understanding that the charter reflects the present consensus about all mODaissues and does not bind any future committee from adapting the Charter to meet theneeds of the circumstances they address.

Moda’s Purposes

• To promote new research topics, joint studies and financial support for researchin the area of experimental design and related topics. This requires the exchangeof new developments and emerging ideas across the whole scientific community.

• To give young researchers the opportunity of establishing personal contacts withleading researchers in the field.

• To bring together active scientists from different statistical schools - particularemphasis is given to the inclusion of scientists from central and eastern Europe.

The Basic Structure

The meetings are strictly of workshop character. Specifically this means the following:

• The number of participants is intended to be around 70, so that everyone gets toknow everyone else.

• The meeting lasts for not more than one week.

• There are no parallel sessions.

• All presentations are the same length (app. 20-30 min.).

• Long breaks for discussion are included.

• The committee may define a number of key themes in advance and suggest invitingparticipants accordingly.

• Participation is by invitation of the committee, as follows:

– Preferred invitation of participants of one of the two preceding workshops toensure continuity.

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Moda Charter mODa8

– Invitees are encouraged to suggest collaborators or students in the event thatthey themselves be unable to attend.

– A number of participants (less than 10) may be nominated by the local or-ganiser.

– Special emphasis should be put on bringing together (and balancing out thenumber of) scientists from EU and non-EU countries and on having around20% of new participants, to guarantee some fluctuation and innovation

– Not only to meet EU funding requirements but also for innovation and reju-venation at least 20 participants should be less than 35 years of age.

• Meetings should take place not more frequently than every third year, to ensurethat material of high quality is presented.

The Proceedings

The proceedings are to be published before the date of the meeting, to allow detaileddiscussion of material which cannot be presented in 20-30 minutes.

• The proceedings of the last six meetings have been published by Physica Verlagit is recommended to keep this collaboration for continuity.

• The main editor is the local organiser of the meeting. It is desirable that oneeditor be a native English speaker.

• All submissions are peer reviewed by at least two referees including at least onecommittee member. The editors have the final decision about acceptance of thepapers.

• The local organising committee has the final decision about the admission of thepaper as a lecture at the workshop.

The Committee

The Committe is in charge of scientific matters, and decides the location, organiser andthe major topics of the next but one workshop in a full meeting at the present workshop.It is formed by:

• Committee members who were present at at least one of the two last workshops.

• Additional persons nominated by the committee, who are present at the currentworkshop, and have either visited at least one of the last two workshops or whoare representatives of major sponsoring organisations.

• The members of the committee are also responsible for refereeing the submittedpapers.

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Moda Charter mODa8

The Organising Committee

The Organising Committee is in charge of organisational matters, and decides the pro-gramme of the workshop. It is formed by:

• The local organisers of the last, current and next meeting.

• Two further board members elected by the board.

And headed by the local organiser. Its special duty is to ensure continuing support bythe funding bodies.

History

This series of meetings was started at Eisenach, former GDR, in 1987, in a somewhatisolated medieval castle with long traditions. There was a good mix of younger and olderscientists and of participants from Western and Eastern Europe countries. Succeedingmeetings have continued to be in relatively isolated locations: St. Kyrik (Bulgaria),Peterhof (Russia), Spetses (Greece), Luminy (France), Puchberg/Schneeberg (Austria)and, most recently, Heeze (The Nederlands). MODA was a vital link between Eastand West during the difficult cold-war period. It has now come of age and traditionsof collaboration and friendship going back 15-20 years can be passed onto a secondgeneration and act as a springboard for future joint research activities.

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Moda Charter mODa8

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PROGRAMME

Conference Programme mODa8

CONFERENCE PROGRAMME

* Speaker

Sunday 3rd

18:00, 19:30 Bus departures to Almagro.

21:00 Vino espanol (Cocktail) in Parador of Almagro.

Monday 4th

9:00-9:30 Opening ceremony.

Chairman: H. P. Wynn

9:30-10:00 Handling Covariates in the Design of Clinical Tri-als by WILLIAM F. ROSENBERGER*, OLEKSANDRSVERDLOV.

10:00-10:30 Investigation of up-and-down strategies for isotonic dose-finding by ANASTASIA IVANOVA*.

10:30-11:00 Coffee break.

11:00-11:30 Recruitment in Multicentre Trials: Prediction and Adjust-ment by VLADIMIR V. ANISIMOV*, DARRYL DOWNING,VALERII V. FEDOROV.

11:30-12:00 Optimal Design of Pharmacokinetic Studies Described byStochastic Differential Equations by VLADIMIR V. ANISI-MOV, VALERII V. FEDOROV, SERGEI L. LEONOV*.

12:00-12:30 Generalized Probit Model in Design of Dose Finding Experi-ments by VALERII V. FEDOROV, YUEHUI WU*.

Chairman: A. Atkinson

15:00-15:30 A Technique for Randomizing Response Adaptive Designs byQUENTIN F. STOUT*, JANIS HARDWICK.

15:30-16:00 Optimal Three-Treatment Response-Adaptive Designs forPhase III Clinical Trials with Binary Responses by ATANUBISWAS*, SAUMEN MANDAL.

16:00-16:30 Sequential, response-adaptive designs driven by a randomlyreinforced urn model by CATERINA MAY*, NANCYFLOURNOY.

16:30-17:00 Coffee break.

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Conference Programme mODa8

17:00-17:30 A new tool for comparing adaptive designs; a poste-riori efficiency by JOSE ANTONIO MOLER*, NANCYFLOURNOY.

17:30-18:00 Model based adaptive design for dose-finding in Phase Iclinical trials by BARBARA BOGACKA*, ANTHONY C.ATKINSON.

19:00-20:00 Theater guided tour.

Tuesday 5th

Chairman: V. Fedorov

9:00-9:30 D-optimal designs for logistic regression in two variables byLINDA M. HAINES*, M. GAETAN KABERA, P. NDLOVU,T. E. O’BRIEN.

9:30-10:00 Bayesian Ds-Optimal Designs for Generalized Linear Mo-dels with Varying Dispersion Parameter by E. RODRIGUESPINTO*, A. PONCE DE LEON.

10:00-10:30 D-optimal Designs for Nonlinear Models Possessing a Cheby-shev Property by VIATCHESLAV MELAS*.

10:30-11:00 Coffee break.

11:00-11:30 Efficient Sampling Windows for Parameter Estimation inMixed Effects Models by MACIEJ PATAN*, BARBARA BO-GACKA.

11:30-12:00 Efficient Nonlinear Experiment Design without any NormalApproximation by EMANUEL WINTERFORS*, ANDREWCURTIS.

14:00-15:00 Committee meeting.

Chairman: A. A. Zhigljavsky

15:00-15:30 Teaching optimal experimental design using a spreadsheet byPETER GOOS*.

15:30-16:00 Optimal designs for rank-order conjoint choice experiments byBART VERMEULEN*, PETER GOOS, MARTINA VAN-DEBROEK.

16:00-16:30 Design of Experiments for Extreme Value Distributions byPATRICK J LAYCOCK*, J. LOPEZ-FIDALGO.

16:30-17:00 Coffee break.

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Conference Programme mODa8

17:00-17:30 Optimal experimental design for hyperparameter estimationin hierarchical linear models with application to marketing byQING LIU, ANGELA DEAN*, GREG ALLENBY.

17:30-18:00 Optimal designs for parameter estimation in stochastic ab-sorbed radiation models by JAVIER VILLARROEL*, JESUSLOPEZ-FIDALGO.

18:00-20:00 Sightseeing at Almagro.

Wednesday 6th

Chairman: B. Torsney

9:00-9:30 Bayes Estimators of Covariance Parameters and the Influenceof Designs by YOUNIS FATHY, CHRISTINE MULLER*.

9:30-10:00 Spatial covariance-robust minimax prediction based on expe-rimental design ideas by GUNTER SPOCK*.

10:00-10:30 A variable-neighbourhood search algorithm for finding op-timal run orders in the presence of serial correlation byJEAN-JACQUES GARROI*, PETER GOOS, KENNETHSORENSEN.

10:30-11:00 Coffee break.

11:00-11:30 D-optimal Designs and Equidistant Designs for StationaryProcesses by MILAN STEHLIK*.

11:30-12:00 Optimal Design for Detecting Spatial Dependence byDANIELA GUMPRECHT, WERNER G. MULLER, JUANM. RODRIGUEZ-DIAZ*.

12:00-12:30 Optimal Designs for the Exponential Model with CorrelatedObservations by ANDREY PEPELYSHEV*.

14:00-23:00 Excursion to Toledo.

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Conference Programme mODa8

Thursday 7th

Chairman: I. Vuchkov

9:00-9:30 Constrained optimal discrimination designs for Fourier re-gression models by STEFANIE BIEDERMANN*, HOLGERDETTE, PHILIPP HOFFMANN.

9:30-10:00 Optimal Designs for Discriminating among Several Non-Normal Models by CHIARA TOMMASI*.

10:00-10:30 A model selection algorithm for mixture experiments inclu-ding process variables by HUGO MARURI-AGUILAR*, EVARICCOMAGNO.

10:30-11:00 Coffee break.

11:00-11:30 Comparisons of Heterogeneity: a Nonparametric Test for theMultisample Case by ROSA ARBORETTI GIANCRISTO-FARO, STEFANO BONNINI*, FORTUNATO PESARIN.

11:30-12:00 On Synchronized Permutation Tests in Two-Way ANOVAby DARIO BASSO*, LUIGI SALMASO, FORTUNATO PE-SARIN.

Chairman: A. Giovagnoli

15:00-15:30 Optimal crossover designs when carryover effects are pro-portional to direct effects by JOACHIM KUNERT*, ROSE-MARY BAILEY.

15:30-16:00 The Within-B-Swap (BS) Design is A- and D-optimalfor estimating the linear contrast for the treatment e-ffect in 3-factorial cDNA microarray experiments by SVENSTANZEL*, RALF-DIETER HILGERS.

16:00-17:30 Coffee poster session.

17:30-18:00 Some Curiosities in Optimal Designs for Random Slopesby THOMAS SCHMELTER*, RAINER SCHWABE, NOR-BERT BENDA.

18:00-18:30 A Comparison of Efficient Designs for Choices Between TwoOptions by HEIKO GROßMANN*, HEINZ HOLLING, UL-RIKE GRAßHOFF, RAINER SCHWABE.

18:30-20:00 Soccer match.

20:30-22:00 Farewell dinner.

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Conference Programme mODa8

Friday 8th

Chairman: W. Muller

9:00-9:30 Optimal Cutpoint Determination: The Case of One PointDesign by THE NGUYEN, BEN TORSNEY*.

9:30-10:00 Asymptotic behaviour of a class of multiplicative algo-rithms of constructing optimal designs by ANATOLY ZHIGL-JAVSKY*.

10:00-10:30 Optimal Orthogonal Three-Level Factorial Designs for Fac-tor Screening and Response Surface Exploration by KENNYYE*, KO-JEN TSAI, WILLIAM LI.

10:30-11:00 Coffee break.

11:00-11:30 Design for a combination of compounds: the balance betweentheory and practice by PETER LANE*, YUEHUI WU.

11:30-12:00 Constructing optimal designs on finite experimental domainsusing methods of mathematical programming by RADOSLAVHARMAN*, MARIA TRNOVSKA, TOMAS JURIK.

12:00 Departure.

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Conference Programme mODa8

Posters

Optimal experimental designs for the test power of radiation intakes by MARIANOAMO-SALAS, JESUS LOPEZ-FIDALGO, JUAN M. RODRIGUEZ-DIAZ.

One-half fractions of a 23 experiment for the logistic model by ROBERTO DORTA-GUERRA, ENRIQUE GONZALEZ-DAVILA, JOSEP GINEBRA.

Optimal Experimental Designs when an independent variable is potentially censored bySANDRA GARCET–RODRIGUEZ, JESUS LOPEZ-FIDALGO.

How ethical are “ethical” designs for clinical trials? A critique and some proposalsof doubly adaptive designs for binary responses by ALESSANDRA GIOVAGNOLI,ALESSANDRO BALDI ANTOGNINI.

A Hierarchical Bayesian Approach to Robust Parameter Design by YURI GOEGE-BEUR, PETER GOOS, MARTINA VANDEBROEK.

Chaotic Behaviour of Multiplicative Algorithms for Constructing Optimal Designs byREBECCA HAYCROFT, ANATOLY ZHIGLJAVSKY.

The influence of the type of the contrast matrix on the optimality of the Within-B-Swap(BS) design in two-channel microarray experiments by RALF-DIETER HILGERS.

Bayesian L-optimal and DA-optimal Design for a Compartmental Model by VICTORIGNACIO LOPEZ RIOS, ROGELIO RAMOS QUIROGA.

Quantile and Probability-level Criteria for Nonlinear Experimental Design by ANDREJPAZMAN, LUC PRONZATO (Speaker: RADOSLAV HARMAN).

Marginally Restricted D-Optimal Designs for correlated observations by JESUS LOPEZ-FIDALGO, RAUL MARTIN-MARTIN, MILAN STEHLIK.

Optimal experimental designs for Cox Regression by JESUS LOPEZ-FIDALGO, MARIAJESUS RIVAS-LOPEZ.

D–Optimal Designs for Regression Models with Length-Biased Poisson Response byISABEL ORTIZ, CARMELO RODRIGUEZ, IGNACIO MARTINEZ.

Determining the Size of Experiments for the One-way ANOVA Model I for OrderedCategorical Data by DIETER RASCH, MARIE SIMECKOVA.

Applications of Optimum Experimental Designs to the Characterization of AdsorptionIsotherms by LICESIO J. RODRIGUEZ-ARAGON, JESUS LOPEZ-FIDALGO.

Optimal Designs for a Modified Exponential Model by JUAN M. RODRIGUEZ-DIAZ,MARIA TERESA SANTOS-MARTIN.

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Conference Programme mODa8

Mixed Poisson fields as models for consumer purchase events by VIPPAL SAVANI,ANATOLY ZHIGLJAVSKY.

QstatLab: software for statistical process control and robust engineering by IVAN N.VUCHKOV.

The Fisher information in nonlinear experimental design by EMANUEL WINTER-FORS.

Bayesian information-based learning by HENRY P. WYNN.

Efficient Conjoint Choice Designs for Mixed Logit Models by JIE YU, PETER GOOS,MARTINA VANDEBROEK.

Optimal designs for Gaussian random fields with exponential correlation structure byMAROUSSA ZAGORAIOU, ALESSANDRO BALDI ANTOGNINI.

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ABSTRACTS

Abstracts mODa8

Handling Covariates in the Design of Clinical Trials

WILLIAM F. ROSENBERGER? and OLEKSANDR SVERDLOVwrosenbe@gmu.edu, osverdlo@gmu.eduGeorge Mason University, U. S. A.

Covariate-adaptive randomization procedures have been proposed to mitigate the impactof covariate imbalances in clinical trials. However, these are often used without a fullunderstanding of their consequences on efficiency and ethical considerations. We giveexamples where balance is inefficient and puts more patients on the inferior treatment.Recent regulatory recommendations have been quite negative about the use of theseprocedures in practice.We compare and contrast two approaches to the problem: ad hoc approaches that tend tobalance but have no formal optimal properties and the optimal design approach favoredby Atkinson, among others. We describe ways in which heterogeneity and randomizationcan be implemented under the optimal design framework. We introduce the concept ofcovariate-adjusted response-adaptive (CARA) randomization procedures.

Investigation of up-and-down strategies for isotonicdose-finding

ANASTASIA IVANOVA?

aivanova@bios.unc.eduUNC at Chapel Hill, USA

We investigate dose-finding strategies in the context of toxicity studies for which it isassumed that toxicity increases with dose. The goal is to identify the maximum tolerateddose, which is taken to be the dose associated with a prespecified target toxicity rate.Group designs are often used for such problems. Usually there are several group designsthat can be employed with a given target. We describe how to choose the best of thesegroup designs. We introduce a new design, the cumulative cohort design, which can bedescribed as a sequence of the best group designs.

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Abstracts mODa8

Recruitment in Multicentre Trials: Prediction andAdjustment

VLADIMIR V. ANISIMOV?

Vladimir.V.Anisimov@gsk.comGlaxoSmithKline, United Kingdom

and

DARRYL DOWNING and VALERII V. FEDOROVdarryl.j.downing@gsk.com, Valeri.V.Fedorov@gsk.comGlaxoSmithKline, U.S.A.

There are a few sources of uncertainty/variability associated with patient recruitmentin multicentre clinical trials: uncertainties in prior information, stochasticity in patientarrival and centre initiation processes. Methods of statistical modeling, prediction andadaptive adjustment of recruitment are proposed to address these issues. The proceduresfor constructing an optimal recruitment design accounting for time and cost constraintsare briefly discussed.

Optimal Design of Pharmacokinetic StudiesDescribed by Stochastic Differential Equations

VLADIMIR V. ANISIMOVVladimir.V.Anisimov@gsk.comGlaxoSmithKline, United Kingdom

and

VALERII V. FEDOROV and SERGEI L. LEONOV?

Valeri.V.Fedorov@gsk.com, Sergei.2.Leonov@gsk.comGlaxoSmithKline, U.S.A.

Pharmacokinetic (PK) studies with serial sampling which are described by compartmen-tal models are discussed. We focus on intrinsic variability induced by the noise terms instochastic differential equations (SDE). For several models of intrinsic randomness, wefind explicit expressions for mean and covariance functions of the solution of the systemof SDE. This, in turn, allows us to construct optimal designs, i.e. find sequences ofsampling times that guarantee the most precise estimation of unknown model parame-ters. The performance of optimal designs is illustrated with several examples, includingcost-based designs.

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Abstracts mODa8

Generalized Probit Model in Design of DoseFinding Experiments

VALERII V. FEDOROV and YUEHUI WU?

Valeri.V.Fedorov@gsk.com, Yuehui.2.Wu@gsk.comGlaxoSmithKline, USA

In clinical studies, continuous endpoints are very commonly seen. However, either forease of interpretation or to simplify the reporting process, some continuous endpointsare often reported and (unfortunately) analyzed as binary or ordinal responses. Weemphasize the usefulness of differentiation between response and utility functions anddevelop tools to build locally optimal designs for corresponding models. It is also shownthat dichotomization of responses may lead to significant loss in statistical precision. Weconsider an example with two responses and one utility function. The generalization toa larger number of responses and utility functions is straightforward.

A Technique for Randomizing Response AdaptiveDesigns

QUENTIN F. STOUT? and JANIS HARDWICKqstout@umich.edu, jphard@umich.eduUniversity of Michigan, USA

Response adaptive designs are rapidly becoming important in a variety of applications,particularly clinical trials. Allocating to reduce the number of poor outcomes, or de-crease cost, or improve power or efficiency measures, are typical of desirable trial objec-tives. Another common goal is randomization to reduce bias. In some cases randomiza-tion is a natural component of the design. However, for many other designs, particularlythose which optimize a given objective, each decision is completely determined once thedesign parameters have been specified and the observations to date are known. Somehave suggested that this deterministic behavior renders most optimal response adaptivedesigns unsuitable for clinical trials or various other applications.Here we introduce randomization in a controlled manner, allowing the designer to spec-ify the tradeoff between randomization and optimization goals for a wide variety ofsettings. For example, one might have a rigid randomization requirement, where thereis a probability 0 ≤ p < 1 such that, at any point in the trial and for any arm (treatmentoption), the probability that the arm will be selected is at least p. Or one might have arandomization goal moderated by ethical concerns, where the extent of randomizationis quite high when the arms have expected success rates that are similar, but is substan-tially reduced when the success rates have a significant difference. Many ad hoc designs

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Abstracts mODa8

intended to maximize successes, such as Thompson’s rule or urn models, have the lat-ter behavior. However, the experimenter has relatively little control over the preciserandomization/objective function tradeoff, especially when the objective involves morethan just the number of successes.Here we use a computational approach to analyze and optimize such tradeoffs. Weshow that there are randomized designs that incur relatively little loss of optimizationobjective, and compare designs optimized for this scenario to randomized optimal de-signs, and to various suboptimal designs. Being able to examine the tradeoff allows theexperimenter to better understand it and select appropriate parameters.The computational approach we use is quite flexible and can accommodate a range ofrandomization goals and rather general optimization goals. Analytic optimization andanalysis in such scenarios appears to be rather difficult, but computationally is quitestraightforward.

Optimal three-treatment response-adaptive designsfor phase III clinical trials with binary responses

ATANU BISWAS?

atanu@isical.ac.inIndian Statistical Institute, Kolkata , India

and

SAUMEN MANDALsaumen.mandal@umanitoba.caUniversity of Manitoba, Winnipeg, Canada

Response-adaptive designs are used in phase III clinical trials to allocate a larger numberof patients to the better treatment. Optimal response-adaptive designs are used for thesame purpose, but the design is derived from some optimal view points. The availableoptimal response-adaptive designs are only for two treatment trials. In the present paper,we extend that idea and derive some optimal response-adaptive designs for phase IIIclinical trials for more than two treatments. In particular, we work on three treatments.The extension is not trivial, as the designs for three treatments are often iterative, andthey need specific algorithms for computation. The proposed approaches are numericallyillustrated, and also some real data set is used to illustrate them.

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Abstracts mODa8

Sequential, response-adaptive designs driven by arandomly reinforced urn model

CATERINA MAY?

cmay@mat.unimi.it

Universita del Piemonte Orientale, Italy

and

NANCY FLOURNOYflournoyn@missouri.edu

University of Missouri, USA

In this study we consider a class of sequential, response-adaptive designs generated by arandomly reinforced urn model introduced in Muliere et al. (2006). These designs gener-alize to responses with discrete or continuous distribution the urn designs proposed in Liet al. (1996) and in Durham et al. (1998) for dichotomous responses. Their performancehas been investigated through numerical simulations in Paganoni and Secchi (2007).Generalized urn schemes have been widely used as models for adaptive-designs (see, forinstance, Rosenberger (2002)). Our scheme is optimal in the sense that units are allo-cated to the superior response with a proportion that converges to one as the numberof patients involved in the experiment increases to infinity. In a clinical trial conductedto compare treatment effects, this property is very desirable from an ethical point ofview; however, the interest of these designs also concerns other areas of applications, forinstance, industrial problems.Consider the following inferential problem: the experimenter wants to test the nullhypothesis that two treatments, say B and W, are equivalent, in the sense that theresponse means µB and µW are equal, against the alternative hypothesis that µB > µW .Most response-adaptive designs considered in literature target an asymptotic allocationproportion ρ ∈ (0, 1), where ρ is usually a function of the unknown parameters of theoutcomes. A comparison between these designs has been considered, for instance, in Huand Rosenberger (2003) and in Zhang and Rosenberger (2006).Because our design is different, in that the asymptotic allocation is 1 if µB > µW andit is a random variable if µB = µW , we need to provide different techniques to studyasymptotic properties. In particular, we resort to the property of stable convergence indistribution for martingales. In May and Flournoy (2006) and in May (2007), the adap-tive estimators of µB and µB are proved to be asymptotically normal and the usual teststatistic ζ0 for comparing the difference of means is studied. The asymptotic normalityof ζ0 is proved when the null hypothesis is true; while, under the alternative hypothesis,the asymptotic distribution of ζ0 is proved to be a specific mixture of normals. Moreover,we provide the exact rate of convergence to infinity of the number of patients assignedto each treatment.

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Abstracts mODa8

References

S. D. Durham, N. Flournoy, and W. Li. A sequential design for maximizing the proba-bility of a favourable response. Canad. J. Statist., 26(3):479–495, 1998.

F. Hu and W.F. Rosenberger. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. Journal of the Amer-ican Statistical Association, 98:671–678, 2003.

W. Li, S. D. Durham, and N. Flournoy. Randomized polya urn designs. Proceedings ofthe Biometric Section of the American Statistical Association, pages 166–170, 1996.

C. May. Asymptotics in a randomly reinforced Polya urn model for sequential, response-adaptive designs. PhD thesis, University of Milan, 2007.

C. May and N. Flournoy. Asymptotics in response-adaptive designs generated by atwo-color, randomly reinforced urn. Preprint, 2006.

P. Muliere, A. Paganoni, and P. Secchi. A randomly reinforced urn. J. Statist. Plann.Inference, 136(6):1853–1874, 2006.

A.M. Paganoni and P. Secchi. A numerical study for comparing two response-adaptivedesigns for continuous treatment effects. Statistical Methods and Applications.

W. F. Rosenberger. Randomized urn models and sequential design. Sequential Analysis,21:1–28, 2002.

L. Zhang and W. F. Rosenberger. Response-adaptive randomization for clinical trialswith continuous responses. Biometrics, 62(2):562–569, 2006.

A new tool for comparing adaptive designs; aposteriori efficiency

JOSE ANTONIO MOLER?

jmoler@unavarra.esPublic University of Navarra, Spain

and

NANCY FLOURNOYflournoyn@missouri.eduUniversity of Missouri, USA

In this work, we consider an adaptive linear regression model designed to explain thepatient’s response in a clinical trial. Patients are assumed to arrive sequentially. The

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Abstracts mODa8

adaptive nature of this statistical model allows the error terms to depend on the pastwhich has not been permitted in other adaptive models in the literature.Some techniques of the theory of optimal designs are used in this framework to define newconcepts: a-posteriori efficiency and mean a-posteriori efficiency. We then explicitlyrelate the variance of the allocation rule to the mean a-posteriori efficiency. Thesemeasures are useful for studying the comparative performance of adaptive designs. Asan example, a comparative study is made among several design-adaptive designs toestablish their properties with respect to a criterion of interest.

Model based adaptive design for dose-finding inPhase I clinical trials

BARBARA BOGACKA?

B.Bogacka@qmul.ac.ukUniversity of London, UK

and

ANTHONY C. ATKINSONA.C.Atkinson@lse.ac.ukLondon School of Economics, UK

The maximum tolerable dose in Phase I clinical trials may not only carry too muchunnecessary risk for patients but may also not be the most efficacious level. This mayoccur when the efficacy of the drug is unimodal rather than increasing, or maybe even bedecreasing, while the toxicity will be an increasing function of the dose. It may be morebeneficial to design a trial so that doses around the so-called Biologically Optimum Dose(BOD) are used more than other dose levels. It is particularly relevant when patients,rather then healthy volunteers, are the first humans to be treated with the new drug,since patients, unlike healthy volunteers, will benefit from a near to optimum treatment.We comment that some novel agents should not be tested on healthy volunteers, par-ticularly when it is expected that the response of a patient might be very different, asmay happen when the new drug stimulates the immune system.Zhang et al. (2006) presented simulation results for an adaptive design for a variety ofmodels when the response is trinomial (“no response”,“success” and “toxicity”). Thechoice of dose for the next cohort depends on the information gathered from previouscohorts, which provides an updated estimate of BOD for the next experiment. However,this reasonable approach is confined to a sparse grid of dose levels which may be farfrom the “true” BOD.In our work we explore the scenarios used by Zhang but search for the BOD over acontinuous dose interval. This increases the percentage of patients treated with a good

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approximation to the “true” BOD. However, more patients may be treated at a hightoxicity probability level and so some further restrictions are introduced to increase thesafety of the trial. We give examples of the properties of various design strategies andsuggest future developments.

References

W. Zhang, D.J. Sargent, and S. Mandrekar. An adaptive dose-finding design incorpo-rating both toxicity and efficacy. Statistics in Medicine, 25:2365–2383, 2006.

D-optimal designs for logistic regression in twovariables

LINDA M. HAINES?

lhaines@stats.uct.ac.zaUniversity of Cape Town, South Africa

M. GAETAN KABERA , P. NDLOVU201291190@ukzn.ac.za, ndlovup@ukzn.ac.zaUniversity of KwaZulu-Natal, South Africa

and

T. E. O’BRIENteobrien@gmail.comLoyola University Chicago, U.S.A.

In this paper locally D-optimal designs for the logistic regression model with two ex-planatory variables, both constrained to be greater than or equal to zero, and no inter-action term are considered. The setting relates to dose-response experiments with doses,and not log doses, of two drugs. It is shown that there are two patterns of D-optimaldesign, one based on 3 and the other on 4 points of support, and that these depend onwhether or not the intercept parameter β0 is greater than or equal to a cut-off value of−1.5434. The global optimality of the designs over a range of β0 values is demonstratednumerically and proved algebraically for the special case of the cut-off value of β0.

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Bayesian Ds-Optimal Designs for Generalized LinearModels with Varying Dispersion Parameter

E. RODRIGUES PINTO?

Edmilson@famat.ufu.brFederal University of Uberlandia, Brazil

and

A. PONCE DE LEONponce@ims.uerj.brRio de Janeiro State University, Brazil

In this article we extend the theory of optimum designs for generalized linear models,addressing the optimality of designs for parameter estimation in a location-dispersionmodel when either not all p parameters in the mean model or not all q parameters inthe dispersion model are of interest. The criterion of Bayesian Ds-optimality is adoptedand its properties are derived. The theory is illustrated with an example from the coffeeindustry.

D-optimal Designs for Nonlinear Models Possessinga Chebyshev Property

VIATCHESLAV MELAS?

v.melas@pobox.spbu.ruSt. Petersburg State University, Russia

The paper is devoted to experimental design for nonlinear regression models, whosederivatives with respect to parameters generate a generalized Chebyshev system. Mostmodels of practical importance possess this property. In particular it is seen in expo-nential, rational and logistic models as well as splines with free knots. It is proved thatsupport points of saturated locally D-optimal designs are monotonic and real analyticfunctions of initial values for those parameters on which models depend nonlinearly. Thisallows one to represent the functions by Taylor series. Similar properties of saturatedmaximin efficient designs are also investigated.

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Efficient Sampling Windows for ParameterEstimation in Mixed Effects Models

MACIEJ PATAN?

M.Patan@issi.uz.zgora.pl

University of Zielona Gora, Poland

and

BARBARA BOGACKAB.Bogacka@qmul.ac.uk

University of London, UK

Optimum experimental design for parameter estimation in mixed effects pharmacoki-netic models has gained considerable attention in the statistical literature. Althoughthe advantage of a high precision of estimation of the population parameters is clear, inadvanced phases of clinical trials when a drug is tested in a population of patients, itmay be impossible to maintain the accurate timing of blood sampling for every patient.This may discourage a practitioner to apply the suggested optimum sampling scheduleand may result in an inefficient experiment and so loss of resources. Sampling windows,that is time intervals assuring some minimum required efficiency, are a good solutionto the problem. Several authors proposed various methods for deriving such windows,based on a design efficiency factor, see Green and Duffull (2003); Graham and Aarons(2006).

The main objective of this work is to give a method of calculating sampling windowsfor mixed effects non-linear models which would not only assure a required minimumefficiency of the population parameter estimation but would also give window size re-flecting the parameter sensitivity, as in Bogacka et al. (2006) who derived such a methodfor calculating sampling windows for a fixed non-liner model. The method is based on acondition of the Equivalence Theorem for D-optimality. It gives less flexibility (narrowerwindows) when it is important to get an observation at a time close to the optimumschedule and more flexibility (wider windows) when it is less important.

References

B. Bogacka, P. Johnson, B. Jones, and O. Volkov. D-efficient window experimentaldesigns. Accepted to JSPI, 2006.

G. Graham and L. Aarons. Optimum blood sampling time windows for parameterestimation in population pharmacokinetic experiments. Statistics in Medicine, 2006.in press.

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B. Green and S.B. Duffull. Prospective evaluation of a D-optimal designed populationpharmacokinetic study. J. of Pharmacokinetics and Pharmacodynamics, 30:145–161,2003.

Efficient Nonlinear Experiment Design without anyNormal Approximation

EMANUEL WINTERFORS?

winterfors@ann.jussieu.frUniversite Pierre et Marie Curie, France

and

ANDREW CURTISAndrew.Curtis@ed.ac.ukEdinburgh University, UK

We present a novel approach to Nonlinear Experimental Design. It aims at minimizingthe expected variance of the posterior probability distribution of an experiment, similarto a Bayesian A-optimal design, but without using any normal (or other) approximationof the posterior distributions. The problem with using the normal approximation toestimate expected variance is that in nonlinear problems some posterior distributionsmight be composed of multiple distant peaks, which make a very large contribution tothe expected variance that will be grossly underestimated using methods that consideronly the variance of each peak separately.

Previous work in this direction include algorithms for maximizing the expected gainin Shannon information defined by Lindley (1956) in the general nonlinear case usingMonte Carlo methods, e.g. Muller (1999), van den Berg et al. (2003) and Ryan (2003),but they have not been applied problems of more than one or two model parametersdue to limited efficiency of the algorithms.

The quality criteria that we suggest are designed with evaluation efficiency in mind.We present also algorithms for their estimation, as well as their optimization. Finallywe demonstrate their efficiency on some high dimensional (> 8) problems, such as thedesign of nonlinear seismic survey methods.

References

D. V. Lindley. On a measure of information provided by an experiment. Ann. Math.Stat., 27(4):986–1005, 1956.

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Peter Muller. Simulation-based optimal design. In Bayesian statistics 6, pages 459–474.Oxford Univ. Press, New York, 1999.

K. J. Ryan. Estimating expected information gains for experimental designs with ap-plication to the random fatigue-limit model. Journal of Computational and GraphicalStatistics, 12(3):585–603, 2003. doi: doi:10.1198/1061860032012.

J. van den Berg, A Curtis, and J. Trampert. Bayesian, nonlinear experimental designapplied to simple, geophysical examples. Geophys. J. Int., 55(2):411–421, 2003.

Teaching optimal experimental design using aspreadsheet

PETER GOOS?

peter.goos@ua.ac.beUniversiteit Antwerpen, Belgium

In this paper, we present an interactive teaching approach to introduce the concept ofoptimal design of experiments to students. Our approach is based on the use of spread-sheets. One advantage of this approach is that no complex mathematical theory isneeded nor that any design construction algorithm has to be discussed at the introduc-tory stage. Another benefit is that the students build all necessary matrices for concreteexamples starting from a sensible initial design. By modifying the initial design by trialand error, they can try to improve the properties of the parameter estimators interac-tively. For problems in which finding the optimal design is not evident, they can useoptimization software which is readily available in the spreadsheet software. Optimaldesign problems for linear as well as for nonlinear models will be discussed.

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Optimal designs for rank-order conjoint choiceexperiments

BART VERMEULEN? , MARTINA VANDEBROEKbart.vermeulen@econ.kuleuven.be, martina.vandebroek@econ.kuleuven.beKatholieke Universiteit Leuven, Belgium

and

PETER GOOSpeter.goos@ua.ac.beUniversiteit Antwerpen, Belgium

In a rank-order conjoint choice experiment, the respondent is asked to rank a numberof alternatives instead of to choose the most preferred one, as is done in standardconjoint choice experiments. The design of the experiment determines the precision ofthe estimated parameters of the rank-ordered multinomial logit model used to analyzethe data. In this paper, we propose a D-optimality criterion to generate Bayesian D-optimal ranking experiments. For this, an expression of the Fisher information matrixof the rank-ordered multinomial logit model is derived which clearly shows how muchadditional information is provided by each extra ranking made by the respondents. Weuse a simulation study to compare the precision of the estimates and the predictiveaccuracy resulting from the Bayesian D-optimal ranking design with a Bayesian D-optimal design for a standard conjoint choice experiment and other commonly-useddesigns. Finally, we examine the different designs based on the improvement in precisionof the estimates and the predictive accuracy yielded by each extra ranking step.

Design of Experiments for Extreme ValueDistributions

PATRICK J. LAYCOCK?

pjlaycock@umist.ac.ukUniversity of Manchester Institute of Science and Technology, UK

and

JESUS LOPEZ-FIDALGOjesus.lopezfidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

There are many situations where extreme values or extreme objectives might affect thedesign of experiments. In this work we consider regression models where the dependent

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variable is an extreme value or has an implied extreme value distribution. Classicexperimental designs, such as factorial designs, fractional and block designs, or responsesurface designs are typically constructed on the assumption of a linear regression modelfor the response variate with additive, finite variance, errors. More specifically, the usualmodel assumes that the data vector y is N(Xθ, σ2I) and we choose X = {x1,x2, ...,xn}T

so as to optimise the estimation of θ in some straightforward way. Such designs aretypically optimised for conditions where ANOVA techniques are used, implying linearity,additivity and finite variance. Fortunately, many designs are known to be useful andrelevant under wide variations on this model. See for example Silvey (1980), Atkinsonand Donev (1992) or Fedorov and Hackl (1997). Our examples will concentrate on thestrength or endurance of materials, where max-stable extreme value distributions forma natural alternative to the Normal family.In this work we study design implications for regression models where the dependentvariable is a measured extreme. Constant variance models are examined and constantcoefficient of variation models are illustrated by an extensive numerical study of a pittingcorrosion data set. A model introduced by Leadbetter et al. (1983) applicable to thestrength of materials is studied and illustrated by an application to designs for examiningthe breaking strength of wide paper strips.

References

A.C. Atkinson and A.N. Donev. Optimum Experimental Designs. Oxford Science Pub-lications, Oxford, 1992.

V.V. Fedorov and P. Hackl. Model-Oriented Design of Experiments. Springer, NewYork, 1997.

M.R. Leadbetter, G. Lindgren, and H. Rootzen. Extremes and Related Properties ofRandom Sequences and Processes. Springer, New York, 1983.

S.D. Silvey. Optimal design. Chapman and Hall, London, 1980.

Optimal experimental design for hyperparameterestimation in hierarchical linear models withapplication to marketing

QING LIU, ANGELA DEAN? and GREG ALLENBYamd@stat.osu.edu, qliu@stat.osu.edu, allenby.1@osu.eduThe Ohio State University, USA

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Optimal design for the efficient estimation of hyperparameters in hierarchical linearmodels is discussed. A criterion is derived under a Bayesian formulation for both thesituation of independent random effects and that of correlated random effects. It isshown by example that designs obtained by fixing the error variance and the randomeffects covariance matrix to the means of their respective prior distributions can be asefficient or almost as efficient as optimal designs obtained by integrating over the priordistributions. We obtain explicit forms of the structure of such optimal designs andstudy the efficiency of exact designs when the optimal structure cannot be achieved.Design robustness is studied under various prior mean specifications of the covariancematrix, and resulting implications for practical applications are discussed.Marketing, and business in general, requires an understanding of when effect sizes areexpected to be large and when they are expected to be small. Gaining an understandingof the contexts in which consumers are sensitive to promotional offers, and to othervariables such as price, is an important aspect of merchandising. Hierarchical modelsare today being used successfully to estimate the importance of product attributes inthe presence of subject heterogeneity. In this talk, experimental designs for the efficientestimation of the hyperparameters in a hierarchical linear model will be discussed andillustrated through a study of the ”level effect” in conjoint analysis. The level effectis the phenomenon, observed in many psychological and marketing studies, that theimportance of a factor as perceived by a respondent increases with the number of levelspresented to that respondent.

Optimal designs for parameter estimation instochastic absorbed radiation models

JAVIER VILLARROEL?

Javier@usal.esUniversity of Salamanca, Spain

and

JESUS LOPEZ-FIDALGOJesus.LopezFidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

We formulate a model to describe the dose of radiation retained by an individual whohas suffered an intake of aerosol radioactive particles. We suppose that a first bioassayis performed in the individual as soon as the accident is detected who is then taken tothe proper place for analysis. We next use this framework to describe two-point optimaldesigns with fixed first point and provide an optimal time t to perform a second bioassay,aiming to estimate the parameters that measure number and size of the intake. It is

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assumed that the mean value of the retention in the respiratory tract can be modeledby a multi-compartmental toxicokinetic model.Let the size of particles leaked be measured by a quantity p and let the parameter I mea-sure the initial intake. We suppose that the fraction of the leak inhaled that is absorbedin the lung is described by a random process {yt}t≥0. Natural a priori requirementson the model are: yt ∈ N with 0 ≤ yt ≤ I, (ii) the trajectory” function t → yt mustbe decreasing and (iii) the present must contain all statistical information necessary todetermine the future; thus {yt} must be a Markov process taking integer values, i.e., acontinuous-time Markov chain. Another natural requirement on the model, condition(iv), is that the average amount of radioactive substance present on the given individ-ual at time t must be proportional to the initial intake, i.e., that E(yt) = If(t, p) forsome f : R2 → R, the “retention function”. Based on the overall Mathematical sim-plicity of the resulting model and actual observations we validate the assumption thatthe response follows a conditional Poisson distribution. We determine the probabilitydistribution of the retention under such a situation and show that the conditional dis-tribution can be taken as Poissonian. The Fisher information matrix follows naturallyfrom these results as

det M(t1, t2) =(ft1;pft2 − ft1ft2;p)

2

ft1ft2

.

where ft1;p is used to indicate the derivative of f with respect to the parameter p attime t1.

Bayes Estimators of Covariance Parameters and theInfluence of Designs

YOUNIS FATHYyounis.fathy@mail.uni-oldenburg.deCarl von Ossietzky University, Germany

and

CHRISTINE MULLER?

cmueller@mathematik.uni-kassel.deUniversity of Kassel, Germany

It is assumed that the covariance matrix of N observations has the form Cθ =∑R

r=1 θr Ur

where U1, . . . , UR are known covariance matrices and θ1, . . . , θR are unknown parameters.Estimators for

∑Rr=1 θr br with known b1, . . . , bR are characterized which minimize the

Bayes risk within all invariant quadratic unbiased estimators. In this characterization,the matrix A, which determines the quadratic form of the estimator, is given by alinear equation system which is not of full rank. It is shown that some solutions of the

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equation system prove to be asymmetric matrices A. Therefore, sufficient conditionsare presented which ensures symmetry of the matrix A. Given this result, the influenceof designs on the Bayes risk is studied.

Spatial covariance-robust minimax prediction basedon experimental design ideas

GUNTER SPOCK?

gunter.spoeck@uni-klu.ac.atUniversity of Klagenfurt, Austria

In spatial statistics literature the so called method of universal kriging is well known. Itis based on best linear prediction in the mean squared error sense in a linear regressionmodel with correlated errors. The covariance structure of the random field thereby mustbe specified by means of an admissible covariance function. Under an assumption ofstationarity of the random field this covariance function is itself estimated from thedata before best linear prediction can take place. Actually the covariance estimate isplugged-in into the best linear predictor which then actually is a non-linear predictor andwhose performance therefore is largely unknown. Performing kriging it is standard upto now to report kriging variances with the covariance function assumed to be known.Actually those variances are estimated too since also here the estimate for the trueunknown covariance function is plugged-in. The consequence is that the report of these“pseudo” variances underestimates the true uncertainties of this plug-in predictor. Thequestion thus is how to take account of the uncertainty of the covariance function inkriging prediction and especially during the report of the uncertainties of this prediction.The present paper/talk will develop a minimax approach where the uncertainty of thecovariance function is taken into account by means of specifying a plausible class ofcovariance functions and determining a linear minimax predictor in such a way that themaximum possible mean squared error of prediction over the whole class of plausiblecovariance functions is minimized. The calculation and derivation of the investigatedminimax predictor makes use of fundamental principles from linear experimental designtheory and therefore fits to the experimental design topics of the conference. Besidestheoretical derivations a real data set based on data from the Tchernobyl accident isinvestigated with the developed methods.

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A variable-neighbourhood search algorithm forfinding optimal run orders in the presence of serialcorrelation

JEAN-JACQUES GARROI?, PETER GOOSJean-Jacques.Garroi@ua.ac.be, Peter.Goos@ua.ac.beUniversiteit Antwerpen, Belgium

and

KENNETH SORENSENKenneth.Sorensen@cib.kuleuven.ac.beKatholieke Universiteit Leuven, Belgium

The responses obtained from a response surface design are typically assumed to beindependent, even when the responses are obtained sequentially. However, it is notdifficult to find practical instances where serial correlations are not negligible.

In this context, determining the order in which an experimental design is run, hasa substantial impact on the precision of the parameters. For that purpose, a goodalgorithm is needed. We propose to use a variable-neighborhood search algorithm todetermine a run order which maximizes the precision of the parameter estimates.

We will apply the algorithm to a situation in which an AR(1) model is suitable to fit thereal correlation structure and a central composite design is used. The GLS estimatorand OLS estimator will be considered. We will focus on the impact of a good run orderin terms of D-efficiency and on the structure of the optimal sequence. Special attentionwill also be paid to large numbers of factors. We will also show how robust our algorithmis.

D-optimal Designs and Equidistant Designs forStationary Processes

MILAN STEHLIK?

Milan.Stehlik@jku.atJohannes Kepler University, Austria

In this talk we discuss the structure of the information matrices of D-optimal experimen-tal designs for the parameters in a stationary process when the parametrized correlationstructure satisfies mild conditions. Such conditions are easily fulfilled by many corre-lation structures, e.g. structures from power exponential family and some members of

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the Matern class. We provide a lower bound for information on the mean parameterand prove it to be an increasing function of distances of design points. The designpoints can collapse under the presence of some covariance structures and a so callednugget effect can be employed in a natural way (see Stehlık et al. (2007)). We also showthat the information of equidistant designs on the covariance parameter is increasingwith the number of design points. If only trend parameters are of interest, the designscovering the whole design space uniformly are rather efficient (see Dette et al. (2007)and Stehlık (2007)). We provide also small sample and asymptotical comparisons ofthe efficiencies of equidistant designs with taking into account both the parameters oftrend θ, as well as the parameters of covariance function r. We concentrate especiallyto Ornstein-Uhlenbeck processes. We are showing that for all possible combinationsof parameters of interest, i.e. {θ}, {r} and {θ, r}, the interval over which observationsare to be made should be extended as far as possible. However doubling the numberof observation points in a given interval, when the only parameter θ is of interest andthere are already a large number of such points, gives practically no additional estima-tion information. When {r} or {θ, r} are the sets of interest, doubling gives the doubleinformation. We show analytically that n-point equidistant design for parameter θ isD-optimal (see Kiselak and Stehlık (2007)). Such a result partially justifies the practiseof equidistantly measured returns derived from time series of stock exchange indexes.

References

H. Dette, J. Kunert, and A. Pepelyshev. Exact optimal designs for weighted least squaresanalysis with correlated errors. Statistica Sinica (accepted), 2007.

J. Kiselak and M. Stehlık. Equidistant d-optimal designs for parameters of ornstein-uhlenbeck process. IFAS research report, 2007.

M. Stehlık. D-optimal designs and equidistant designs for stationary processes. mODa8 Proceedings, 2007.

M. Stehlık, J.M. Rodrıguez-Dıaz, W.G. Muller, and J. Lopez-Fidalgo. Optimal alloca-tion of bioasseys in the case of parametrized covariance functions: an application inlung’s retention of radioactive particles. TEST (in press), 2007.

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Optimal Design for Detecting Spatial Dependence

DANIELA GUMPRECHTdaniela.gumprecht@wu-wien.ac.atUniversity of Economics Vienna, Austria

WERNER G. MULLER?

werner.mueller@jku.atJ.Kepler-University Linz, Austria

and

JUAN M. RODRIGUEZ-DIAZjuanmrod@usal.esUniversity of Salamanca, Spain

The aim of this paper is to find optimal or nearly optimal designs for experiments todetect spatial dependence that might be in the data. The question to be answeredis, how to optimally select predictor values to detect the spatial structure - if it isexistent, and how to avoid to spuriously detect spatial dependence if there is no suchstructure. The starting point of this analysis are two different linear regression models(1) an ordinary linear regression model with i.i.d. error terms - the non-spatial case,and (2) a regression model with a spatially autocorrelated error term, a so called spatialautoregressive error model (SAR error model). The procedure can be divided into twomain parts: firstly, use of an exchange algorithm to find the optimal design for therespective data collection process; for its evaluation an artificial data set was generatedand used. Secondly, estimation of the parameters of the regression model and calculationof Moran’s I which is used as an indicator for spatial dependence in the data set. Themethod is illustrated by applying it to a well-known case study in spatial analysis.

Optimal Designs for the Exponential Model withCorrelated Observations

ANDREY PEPELYSHEV?

andrey@ap7236.spbu.ruSt. Petersburg State University, Russia

In the exponential regression model with an autoregressive error structure exact D-optimal designs for weighted least squares analysis are investigated. It is shown thatsupport points of a locally D-optimal design are discontinuous with respect to the cor-relation parameter. Also equidistant designs are proved to be considerably less efficientthan maximin efficient D-optimal designs.

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Constrained optimal discrimination designs forFourier regression models

STEFANIE BIEDERMANN?

S.Biedermann@soton.ac.ukUniversity of Southampton, Great Britain

and

HOLGER DETTE and PHILIPP HOFFMANNHolger.Dette@rub.deRuhr-University Bochum, Germany

In this talk, the problem of constructing efficient discrimination designs between Fourierregression models of different degrees will be considered. We investigate designs whichmaximize the power of the F -test, which discriminates between the two highest ordermodels, subject to the constraints that the tests that discriminate between lower ordermodels have at least some given relative power. A complete solution is presented interms of the canonical moments [see, e.g., Dette and Studden (1997)] of the optimaldesigns, and for the special case of equal constraints even more specific formulae for theoptimal support points and weights are available; see Biedermann et al. (2007).

References

S. Biedermann, H. Dette, and P. Hoffmann. Constrained optimal discrimination de-signs for fourier regression models. accepted in: Annals of the Institute of StatisticalMathematics, 2007.

H. Dette and W. Studden. The theory of canonical moments with applications in statis-tics, probability and analysis. Wiley, New York, 1997.

Optimal designs for discriminating among severalnon-Normal models

CHIARA TOMMASI?

chiara.tommasi@unimi.itUniversity of Milano, Italy

Many results on optimal experimental designs are derived under the assumption that thestatistical model is known at the design stage. Thus, the purpose of the experiment is toestimate a specific aspect of that model. However, rarely the researcher is confident that

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a particular model underlies the data. In this paper several rival models are assumedto be available and the purpose of the experiment is to determine which of the modelsis the more adequate.In order to check the adequacy of a linear regression model, Atkinson (1972) proposesto embed the model in a more general model and to design to estimate the additionalparameters in the best way. Atkinson and Cox (1974) generalize this approach to thecase of comparing several linear models. Another method for discriminating betweentwo or more regression models is the T-criterion proposed by Atkinson and Fedorov(1975a,b). This criterion is based on the assumption that the random errors of themodel are Gaussian and homoscedastic. A generalization of the T-optimality criterionfor heteroscedastic models is provided by Ucinski and Bogacka (2004). Another gener-alization of the T-criterion for discriminating between two generalized linear models isprovided by Ponce de Leon and Atkinson (1992). In order to deal with any distribu-tion for the random errors, Lopez-Fidalgo et al. (2007) propose a new criterion basedon the Kullback-Liebler distance. This new criterion is called KL-criterion and is verygeneral. It includes as special cases the T-criterion (homoscedastic case) and the gener-alization provided by Ucinski and Bogacka (2004) (heteroscedastic case), whenever theerror distribution is Normal. Furthermore, it includes the proposal of Ponce de Leonand Atkinson (1992) in the case of two generalized linear models.In this paper, a generalization of the KL-criterion is proposed to deal with the discrim-ination among several non-Normal models. An example where three logistic regressionmodels are compared is provided.

References

A. C. Atkinson and D.R. Cox. Planning experiments for discriminating between models.J.R. Statist. Soc. B, 36:321–348, 1974.

A. C. Atkinson and V.V. Fedorov. The designs of experiments for discriminating betweentwo rival models. Biometrika, 62:57–70, 1975a.

A. C. Atkinson and V.V. Fedorov. Optimal design: experiments for discriminatingbetween several models. Biometrika, 62:289–303, 1975b.

A.C. Atkinson. Planning experiments to detect inadequate regression models.Biometrika, 59:275–293, 1972.

J. Lopez-Fidalgo, C. Tommasi, and P.C. Trandafir. An optimal experimental designcriterion for discriminating between non-normal models. J.R.Statist.Soc B, 69(2):1–12, 2007.

A.C Ponce de Leon and A.C. Atkinson. The design of experiments to discriminate

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between two rival generalized linear models. In Lecture Notes in Statistics - Advancesin GLM and Statistical Modelling, pages 159–164. Springer-Verlag, New York, 1992.

D. Ucinski and B. Bogacka. T-optimum designs for multiresponse heteroscedastic mod-els. In mODa 7 - Advances in Model-Oriented Design and Analysis, pages 191–199),Heidelberg, New York, 2004. Physica-Verlag.

A model selection algorithm for mixtureexperiments including process variables

HUGO MARURI-AGUILAR?

H.Maruri-Aguilar@lse.ac.ukLondon School of Economics, UK

and

EVA RICCOMAGNOriccomag@dima.unige.itUniversita di Genova, Italy

Experiments with mixture and process variables are often constructed as the cross prod-uct of a mixture and a factorial design. Often it is not possible to implement all the runsof the cross product design, or the cross product model is too large to be of practicalinterest.We propose a methodology to select a model with a given number of terms and minimalcondition number. The search methodology is based on weighted term orderings andcan be extended to consider other statistical criteria.

Comparisons of Heterogeneity: a NonparametricTest for the Multisample Case

ROSA ARBORETTI GIANCRISTOFARO, STEFANO BONNINI?

rosa.arboretti@unife.it, bnnsfn@unife.itUniversity of Ferrara, Italy

and

FORTUNATO PESARINfortunato.pesarin@unipd.itUniversity of Padova, Italy

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Abstracts mODa8

In several scientific disciplines it is often of interest to compare the concentration ofthe distribution of a categorical variable between two or more populations. The aim isto establish if the heterogeneities of the distributions are equal or not. We propose anonparametric solution based on a permutation test. The main properties of the testand a Monte Carlo simulation in order to evaluate its behaviour will be discussed.

On Synchronized Permutation Tests in Two-WayANOVA

DARIO BASSO?, FORTUNATO PESARIN and LUIGI SALMASOdario@stat.unipd.it, fortunato.pesarin@unipd.it, salmaso@gest.unipd.itUniversity of Padova, Italy

In I×J balanced factorial designs units are not exchangeable between blocks since theirexpected values depend on received treatments. It does not seem possible, therefore, toobtain exact and separate tests to respectively assess main factor and interaction effects.Parametric two-way ANOVA F tests are exact tests only under assumption of normalhomoscedastic errors, but they are also positively correlated. Instead, it is possibleto obtain exact, separate and uncorrelated permutation tests at least for main factorsby introducing a restricted kind of permutations, named synchronized permutations.Since these tests are conditional on observed data, they are distribution-free and maybe shown to be almost as powerful as their parametric counterpart under normal errors.We obtain the expression of the correlation between the main factor ANOVA tests as afunction of the number of replicates in each block, the number of main factor levels andtheir noncentrality parameters.

Optimal crossover designs when carryover effectsare proportional to direct effects

JOACHIM KUNERT?

joachim.kunert@udo.eduUniversitat Dortmund, Germany

and

ROSEMARY BAILEYr.a.bailey@qmul.ac.ukUniversity of London, U.K.

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In Bailey and Kunert (2006) we considered optimality of crossover designs in a modelwhere carryover effects are proportional to direct effects. The optimality was provedwith a generalization of a method used in Kunert and Martin (2000). Bailey and Kunert(2006) restricted attention to the case where the proportionality factor was relativelysmall. In that case, it was possible to show that so-called totally balanced designs areuniversally optimal. In a totally balanced design no treatment is directly preceded byitself. In the present paper, we consider the case where the proportionality factor getsrelatively large. Applying the methods used in Bailey and Kunert (2006) and computeralgebra, we can show that designs with pairs of consecutive identical treatments performbetter.

References

R.A. Bailey and J. Kunert. On optimal crossover designs when carryover effects areproportional to direct effects. Biometrika, 93:613–625, 2006.

J. Kunert and R.J. Martin. On the determination of optimal designs for an interferencemodel. Ann. Statist., 28:1728–1742, 2000.

The Within-B-Swap (BS) Design is A- andD-optimal for estimating the linear contrast for thetreatment effect in 3-factorial cDNA microarrayexperiments

SVEN STANZEL? and RALF-DIETER HILGERSsstanzel@ukaachen.de, rhilgers@ukaachen.deInstitute for Medical Statistics, RWTH Aachen, Germany

cDNA microarrays are a powerful tool in gene expression analysis (Speed, 2003). Land-grebe (Landgrebe et al., 2006) proposed a special 3-factor model to estimate variouseffects on the log ratios of measured fluorescence intensities. We demonstrate in thistalk that the Within-B-Swap (BS) design introduced by Landgrebe (Landgrebe et al.,2006) is A- and D-optimal for estimating the linear contrast for the treatment effect ingeneral situations of l treatments and k cell lines.

References

J. Landgrebe, F. Bretz, and E. Brunner. Efficient design and analysis of two colourfactorial microarray experiments. Computational Statistics and Data Analysis, 2006.

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T. Speed. Statistical analysis of gene expression microarray data. Chapman and Hall,Boca Raton, 2003.

Some Curiosities in Optimal Designs for RandomSlopes

THOMAS SCHMELTER?, RAINER SCHWABEThomas.Schmelter@schering.de, rainer.schwabe@mathematik.uni-magdeburg.deOtto-von-Guericke-University, Germany

and

NORBERT BENDAnorbert.benda@novartis.comNovartis Pharma AG, Switzerland

The purpose of this note is to show by a simple example that some of the favorite resultsin optimal design theory do not necessarily carry over if random effects are involved. Inparticular, the usage of the popular D-criterion appears to be doubtful.

A Comparison of Efficient Designs for ChoicesBetween Two Options

HEIKO GROßMANN?

h.grossmann@qmul.ac.ukUniversity of London, United Kingdom

HEINZ HOLLINGholling@psy.uni-muenster.deWestfalische Wilhelms-Universitat Munster, Germany

and

ULRIKE GRAßHOFF and RAINER SCHWABEulrike.grasshoff@mathematik.uni-magdeburg.de,

rainer.schwabe@mathematik.uni-magdeburg.deOtto-von-Guericke-Universitat Magdeburg, Germany

Optimal designs for choice experiments with choice sets of size two are frequently derivedunder the assumption that all model parameters in a multinomial logit model are equalto zero. In this case, optimal designs for linear paired comparisons are also optimal for

45

Abstracts mODa8

the choice model. It is shown that the methods for constructing linear paired comparisondesigns often require a considerably smaller number of choice sets when the parametersof primary interest are main effects

Optimal Cutpoint Determination: The Case of OnePoint Design

THE NGUYEN and BEN TORSNEY?

the@stats.gla.ac.uk, bent@stats.gla.ac.ukUniversity of Glasgow, Scotland

The paper briefly describes results on determining optimal cutpoints in a survey ques-tion. We focus on the case when we offer all respondents a set of cutpoints: a one pointdesign. Applications in the social sciences will be cited, including contingent valuationstudies, which aim to assess a population’s willingness to pay for some service or amenity,and in market research studies. The problem will be formulated as a generalized linearmodel. The formula for the Fisher information matrix is constructed. Search methodsare used to find optimal solutions. Results are reported and illustrated pictorially.

Asymptotic behaviour of a class of multiplicativealgorithms of constructing optimal designs

ANATOLY ZHIGLJAVSKY?

ZhigljavskyAA@cf.ac.ukCardiff University, UK

Consider the common regression model y = θT f(x)+ε, where θ is a vector of parameters,f(x) is a vector of base functions and x belongs to a finite set X = {x1, . . . , xn} (thedesign space). For a design ξ giving weights ξ(xi) to the points xi (i = 1, . . . , n), wedefine the information matrix

M(ξ) =n∑

i=1

ξ(xi)f(xi)f(xi)T ,

the optimality criterion Φ(M(ξ)) (to be optimized with respect to ξ) and the function

ϕ(x, ξ) = fT (x)◦Φ(ξ)f(x) where

◦Φ(ξ) =

∂Φ

∂M

∣∣∣∣M=M(ξ)

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Abstracts mODa8

(we assume that the functional Φ is differentiable).We consider the class of multiplicative updating of the weights of the designs:

ξr+1(x) =ϕ(x, ξr)− cr

br

ξr(x) (r = 0, 1, . . .), (1)

where br are normalising constants br = tr[M(ξ)

◦Φ(ξr)

]− cr and cr are parameters of

the algorithm. Different versions of algorithm (1) have been considered by Ben Torsneyand many other authors.We discuss some asymptotic properties of the algorithm (1). The discussion is split asfollows:

(a) studying the monotonicity of the sequence Φ(M(ξr)) for the D-optimality criterion;

(b) creating chaotic behaviour of the sequence (1) for the simple linear regression withf(x) = (1, x)T implying construction of efficient gradient algorithms for quadraticoptimization in Rn;

(c) numerical study.

The results on (a) are joint with H.Dette and A.Pepelyshev; the importance of theresearch has been inspired by B.Torsney and L. Pronzato. The results on (b) are jointwith L.Pronzato and H.P.Wynn. The results on (c) are joint with R.Haycroft.

Optimal Orthogonal Three-Level Factorial Designsfor Factor Screening and Response SurfaceExploration

KENNY YE?

kye@aecom.yu.eduAlbert Einstein College of Medicine, New York, USA

KO-JEN TSAIkojen-tsai@gmail.comYes Solutions, New York, USA

and

WILLIAM LIwli@cmos.umn.eduUniversity of Minnesota, Minneapolis, USA

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Abstracts mODa8

Three-level factorial designs can be used to perform factor screening and subsequentlyresponse surface exploration on its projections in a single stage experiment. Here weselect optimal designs for this approach from 18-run and 27-run orthogonal designs.Our choices are made based on two types of design criteria. Besides commonly usedmodel estimation criteria, we also consider model discrimination criteria. For 18-rundesigns, the recently constructed catalog allows us to examine all possible orthogonaldesigns. Since none of the OA(18,37) designs have full EC, non-orthogonal designs mightbe considered to accommodate 7 three-level factors. For 27-run designs, we examinedprojections of three OA(27,313)s.

Design for a combination of compounds: the balancebetween theory and practice

PETER LANE?

Peter.W.Lane@gsk.comGlaxoSmithKline, UK

and

YUEHUI WUYuehui.2.Wu@gsk.comGlaxoSmithKline, US

Studying drug combinations is becoming of greater interest in the pharmaceutical in-dustry. Usually, the investigators do not know whether or not there will be interactionsbetween the effects of the compounds so the design should give the opportunity to exam-ine different combined dosage levels to investigate possible interactions. The practicalproblem considered here is a Phase IIB study for two drugs LABA and ICS with threedose levels for each and the goal of the study is to construct a design such that thewidth of 95% CI for any dose combination is smaller than a given value using the small-est sample size possible. The response is continuous and the model under considerationis

F = µ + αI + βI2 + γL + δL2 + θLI + ε. (1)

It’s a well-known result that for a linear model like (1), the D-optimal design can achievethe accuracy of 95% CI with the least number of subjects. Furthermore, D-optimaldesign doesn’t depend on the unknown parameters in the model. However, in practice,a variety of constraints required by a clinical project team need to be incorporated inthe design such as minimum subjects should be assigned to a certain treatment or acertain treatment should be included in the design. The theoretical D-optimal designwill serve as the benchmark for other practical/modified designs. We will discuss severalpractical designs that can be applied for this trial and illustrate how effective they are

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Abstracts mODa8

in reaching the study goal compared to the D-optimal design; these include a trial-and-error method using Monte Carlo simulation, and an automated method based onoptimal design methodology.

Constructing optimal designs on finite experimentaldomains using methods of mathematicalprogramming

RADOSLAV HARMAN?, MARIA TRNOVSKA and TOMAS JURIKharman@fmph.uniba.sk, trnovska@fmph.uniba.sk, jurik@fmph.uniba.skComenius University Bratislava, Slovakia

In the talk we will give a survey of selected optimal design problems on finite experimen-tal domain that can be solved as special cases of linear and semidefinite programming,or the so-called maxdet problem of mathematical optimization (see Vandenberghe et al.(1998)). With focus on c- and D-optimality, we will present problems of optimal designunder various constraints on the design composition or multiobjective efficiency. Wewill conclude the talk by a discussion of general algorithms of mathematical program-ming, such as the simplex method or the interior point method, used as alternatives totraditional algorithms for constructing designs of experiments.

References

L. Vandenberghe, S. Boyd, and S. Wu. Determinant maximization with linear matrixinequality constraints. SIAM Journal on Matrix Analysis and Applications, 19:499–533, 1998.

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Optimal experimental designs for the test power ofradiation intakes

MARIANO AMO-SALAS? , JESUS LOPEZ-FIDALGOMariano.Amo@uclm.es, Jesus.LopezFidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

and

JUAN M. RODRIGUEZ-DIAZjuanmrod@usal.esUniversity of Salamanca, Spain

The model that describes the retention in the lungs of the radioisotope particles will bestudied. The framework is a situation of an accident in facilities that handle radioactivematerials. Optimal times to make the bioassays are calculated. The criteria used areD-optimality and c-optimality. Efficiencies for the computed designs are provided andcompared. Moreover, the test power is calculated by means of simulations and repli-cations. Then the inverse of the Fisher information matrix will be compared with anestimation of the covariance matrix of the parameters.

One-half fractions of a 23 experiment for the logisticmodel

ROBERTO DORTA-GUERRA? , ENRIQUE GONZALEZ-DAVILArodorta@ull.es, egonzale@ull.esUniversidad de La Laguna, Spain

and

JOSEP GINEBRAjosep.ginebra@upc.eduUniversitat Politecnica de Catalunya, Spain

D-optimal experiments for binary response data have been extensively studied in recentyears (Sitter and Torsney (1995), Ford et al. (1992) and Dorta-Guerra et al. (2005)).On the other hand two-level fractional factorials are very used as screening designs atthe preliminary stages of an investigation when the outcome is continuous. We explorethe performance of the one-half two-level experiments for a logistic model with threefactors, and show that conventional wisdom about this kind of experiments does notapply when the response is binomial.

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References

R. Dorta-Guerra, E. Gonzalez-Davila, and J. Ginebra. Two-level experiments for binaryresponse data. Universidad Politecnica de Cataluna, Barcelona, 2005.

I. Ford, B. Torsney, and C.F.J. Wu. The use of canonical form in the construction oflocally optimal designs for non-linear problems. J. of the Royal Statistical Society, 54:569–583, 1992.

R.R. Sitter and B. Torsney. Optimal designs for binary response experiments with twodesign variables. Stat. Sinica, 5:405–419, 1995.

Optimal Experimental Designs when anindependent variable is potentially censored

SANDRA GARCET-RODRIGUEZ?

sandra garcet@usal.esUniversity of Salamanca, Spain

and

JESUS LOPEZ-FIDALGOjesus.lopezfidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

In the classical theory of optimal experimental design for linear models it is usuallyassumed that the experimenter can perform an experiment at any precise value of theindependent variables within the whole design space. Nevertheless, in many areas ofapplication it is common to find an independent variable that may be censored. Forexample, Varela et al. (2001) applied an exercise test to obtain more information topredict surgery complications in the treatment of lung cancer. The test consists on ridinga static bicycle using a medical protocol. There are several independent variables, butthe exercise time in minutes is the only one that can be controlled by the experimenter.In practice, a target exercise time is assigned to a patient, but he or she may stop theexercise before the time is over. It is supposed here that the stopping reasons are non-informative for the prediction. It will be assumed that the censoring of this variable hasa known distribution. This means that the experimental design for this variable willbe censored. In this case the experiment must be designed according to the censoreddistribution.Garcet-Rodrıguez et al. (2007) dealt with the problem of obtaining optimal approximatedesigns for a linear model when the values of some independent variables are potentiallycensored according to a known probability distribution function. They considered theproblem for a discrete space. The continuous case needs a different approach that is

51

Abstracts mODa8

considered in this work. Appropriate algorithms are provided for computing optimaldesigns in both the discrete and the continuous cases.Let t denote a time variable potentially censored in a design space χ. A time variableis used here as an illustrative and typical case for this problem, but the results maybe applied to any other kind of variable t. The censoring distribution will be assumedknown through the random variable T , which measures the time a chosen experimentalunit is going to stop given no prior limitation in time. In the real case mentioned aboveT would be the time a generic patient stops if he or she starts to ride the bicycle withoutany time limit imposed in advance. A probability distribution of the censored time Twill be assumed on a set, which includes the whole design space. A particular, buttypical case, may be a distribution on [0,∞) with a design space contained in it, e.g.χ = [0, b].Let ξ be the approximate design with finite support that is intended to be appliedin practice. Due to censoring another design ξ is expected to result at the end of theexperimentation. Therefore, a design ξ should be found such that the expected censoringrestricted design ξ will be optimal among all possible expected designs. We will call anoptimal design ξ? with this constraint censoring restricted (CER) optimal design whileξ? will be the expected censoring restricted (ECER) optimal design. Sometimes it ispossible to find ξ such that the expected design ξ will be optimum according to thecriterion without censoring. But frequently this is not the case and a restricted searchhas to be performed.The two possible cases with either a finite or a continuous design space are consideredand algorithms for the computation of these designs are provided.

References

S. Garcet-Rodrıguez, J. Lopez-Fidalgo, and R. Martın-Martın. Some complexities inoptimal experimental designs introduced by real life problems. Tatra Mt. Math. Publ.,(to appear), 2007.

G. Varela, R. Cordovilla, M.F. Jimenez, and N. Novoa. Utility of standarized exerciseoximetry to predict cardiopulmonary morbidity after lung resection. European Journalof Cardio–thoracic Surgery, 19:351–354, 2001.

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Abstracts mODa8

How ethical are “ethical” designs for clinical trials?A critique and some proposals of doubly adaptivedesigns for binary responses

ALESSANDRA GIOVAGNOLI? and ALESSANDRO BALDI ANTOGNINIalessandra.giovagnoli@unibo.it, baldi@stat.unibo.itUniversity of Bologna, Italy

The whole field of clinical trials for treatment comparison is torn between minimizingpotential harm to the patients presently under care and maximizing experimental infor-mation to establish which is the superior treatment. This dilemma is often referred toas individual-versus-collective ethics. Many “ethical” criteria have being suggested fordesigning such trials for treatment comparison. In this paper we review and discuss therecent literature, focussing on doubly adaptive sequential designs for binary responses(sequential experiments are said to be adaptive if the observed responses are used tomodify the experiment as we go along; we call them doubly adaptive when the pastdesign history is also taken into account). We put forward a compound criterion andintroduce a sequential procedure consistent with this criterion. We compare the proper-ties of such a procedure with those of the designs proposed by Rosenberger et al. (2001)and Geraldes et al. (2006).

References

M. Geraldes, V. Melfi, C. Page, and H. Zhang. The doubly adaptive weighted differencesdesign. Journal of Statistical Planning and Inference, 136:1923–1939, 2006.

W.F. Rosenberger, N. Stallard, A. Ivanova, C.N. Harper, and M.L. Ricks. Optimaladaptive designs for binary response trials. Biometrics, 57:909–913, 2001.

53

Abstracts mODa8

A Hierarchical Bayesian Approach to RobustParameter Design

YURI GOEGEBEURyuri.goegebeur@stat.sdu.dkUniversity of Southern Denmark, Denmark

PETER GOOSpeter.goos@ua.ac.beUniversiteit Antwerpen, Belgium

and

MARTINA VANDEBROEKmartina.vandebroek@econ.kuleuven.beK.U.Leuven, Belgium

The goal of robust parameter design experiments is to identify significant location anddispersion factors that can be used to set the mean response at the target level andto decrease the sensitivity of the response to uncontrolled noise factors. We present ahierarchical Bayesian model and use empirical Bayesian priors to find the active factorsand to get reliable estimates of the location and dispersion parameters. The approachcan also be used if the design points are not replicated which makes the model selectionproblem challenging with standard procedures.

Chaotic Behaviour of Multiplicative Algorithms forConstructing Optimal Designs

REBECCA HAYCROFT and ANATOLY ZHIGLJAVSKYhaycroftRJ@cf.ac.uk, zhigljavskyAA@cf.ac.ukCardiff University, UK

We demonstrate that many multiplicative algorithms for constructing optimal designsbehave chaotically and converge to neither an optimal design nor any other.

54

Abstracts mODa8

The influence of the type of the contrast matrix onthe optimality of the Within-B-Swap (BS) design intwo-channel microarray experiments

RALF-DIETER HILGERSrhilgers@ukaachen.deInstitute for Medical Statistics, RWTH Aachen, Germany

Two-channel microarray experiments can be analyzed by fitting theanalysis of variance model recently introduced by Landgrebe (Landgrebe et al., 2006) tothe observed fluorescence intensities. The model allows the investigation of gene specifictreatment effects by using intrablock comparisons. Stanzel and Hilgers (Stanzel andHilgers, 2007) showed that the Within-B-Swap (BS) design which allocates all pairwisedifferent treatment combinations to the two different colors (channels) is A- and D-optimal for estimating the linear contrast of all pairwise treatment comparisons.Within the talk we discuss the influence of the type of contrast on the optimality of theWithin-B-Swap (BS) design. We will show that, if l treatments and a contrast matrixwith column sum 0 and rank = l − 1 are used, the Within-B-Swap (BS) design will beD-optimal. Counterexamples to the rank condition will also be given.

References

J. Landgrebe, F. Bretz, and E. Brunner. Efficient design and analysis of two colourfactorial microarray experiments. Computational Statistics and Data Analysis, 2006.

S. Stanzel and R.D. Hilgers. The within-b-swap (bs) design is a- and d-optimal forestimating the linear contrast for the treatment effect in 3-factorial cdna microarrayexperiments. Proceedings of the 8th international workshop on Model-Oriented Designand Analysis in Almagro, Spain, June 4-8, 2007.

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Abstracts mODa8

Bayesian L-optimal and DA-optimal Design for aCompartmental Model

VICTOR IGNACIO LOPEZ RIOS?

vilopez@cimat.mxUniversidad Nacional de Colombia sede Medellın, Colombia.

and

ROGELIO RAMOS QUIROGArramosq@cimat.mxCentro de Investigacion en Matematicas, CIMAT, Guanajuato, Gto. Mexico

Compartmental models are used in pharmacokinetics where the exchange of materialsin biological systems is studied, (Clark and Smith (1989)). In this work, we consider acompartmental model with four components and reversible rates of transfer in the last

two components,(A

θ5→ Dθ1→ Bθ2

θ3C

θ4→). We find optimal experimental design for a

nonlinear model arising in the last compartment, C, (for similar works see Atkinson et al.(1993), Allen (1983), Stroud et al. (2001) and Waterhouse (2005)). The optimizationis performed with respect to various criteria which depend on the Fisher informationmatrix. Special attention is given to Bayesian L-optimal design and Bayesian DA-optimal design (generalized determinant criterion) in order to obtain optimal samplingtimes for estimating several nonlinear functions of the parameters (rates of transfer) asthe total area under the concentration curve, the maximum concentration and the timeto maximum concentration (Atkinson and Donev (1992)). Several prior distributionsare used for both criteria and we obtain all optimal designs by using the algorithmsproposed in Fedorov and Hackl (1997). Also, for all of them the efficiencies are providedand compared.

References

D. M. Allen. Parameter estimation for nonlinear models with emphasis on compartmen-tal models. Biometrics, 39:629–637, 1983.

A. C. Atkinson and A. N. Donev. Optimum Experimental Designs. Oxford UniversityPress, New York, 1992.

A. C. Atkinson, K. Chaloner, A. M. Herzberg, and J. Juritz. Optimum experimentaldesigns for properties of a compartmental model. Biometrics, 49 (2):325–337, 1993.

B. Clark and D. A. Smith. An Introduction to Pharmacokinetics. Oxford, England,1989.

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V. V. Fedorov and P. Hackl. Model-Oriented Design of Experiments. Springer-Verlag,New York, 1997.

J. R. Stroud, P. Muller, and G. L. Rosner. Optimal sampling times in populationpharmacokinetic studies. Appl. Statist., 50 Part 3:345–359, 2001.

T. H. Waterhouse. Optimal Experimental Design for Nonlinear and Generalised LinearModels. PhD thesis, University of Queensland, Australia, 2005.

Quantile and Probability-level Criteria forNonlinear Experimental Design

ANDREJ PAZMANpazman@center.fmph.uniba.skComenius University, Slovakia

and

LUC PRONZATOpronzato@i3s.unice.frUniversite de Nice–Sophia Antipolis, France

We consider optimal experimental design for parameter estimation in nonlinear situ-ations where the optimal experiment depends on the value of the parameters to beestimated. Setting a prior distribution for these parameters, we construct criteria basedon quantiles and probability levels of classical design criteria and show how their deriva-tives can easily be approximated, so that classical algorithms for local optimal designcan be used for their optimisation.

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Construction of Marginally Restricted D-OptimalDesigns for correlated observations

RAUL MARTIN-MARTIN? , JESUS LOPEZ-FIDALGORaul.MMartin@uclm.es, Jesus.LopezFidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

and

MILAN STEHLIKMilan.Stehlik@jku.atJohannes Kepler University, Austria

In the real life practice a model typically involves variables that are under the control ofthe experimenter as well as other variables that are uncontrollable. This situation adds anew degree of complexity to the optimal experimental design theory and practice. Whensome of the variables in the model are not under control and their values are knownin advance the search of the optimal design has to be constrained to the marginaldesigns given by those values. These designs are called marginally restricted (MR)designs. Cook and Thibodeau (1980) introduced the idea of MR D-optimal designsand Nachtsheim (1989) provided equivalence theorems and algorithms for D-optimalityand Ds-optimality. Huang and Hsu (1993) generalized these results for more generalcriterion functions. Lopez-Fidalgo and Garcet-Rodrıguez (2004) proved the convergenceof the algorithms for a class of criteria and provided a new background with uncontrolledvariables whose values are only known after the experiment is realized.

Another usual situation in practice is that the responses may be correlated as it is thecase of spatial observations or repeated measurements. For instance, spatial data areusually positively spatially correlated which represents the fact that observations fromnearby sites tend to be more alike. From optimal experimental design theory this isan important challenge that has been treated in the literature in a small scale. Somereferences of it may be found e.g. in Brimkulov et al. (1980), Abt and Welch (1998),Cressie (1993) or Ucinski and Atkinson (2004).

The combination of this two practical aspects are considered. From a theoretical back-ground some ways to compute optimal designs are provided. From a practical point ofview designs are computed for different real life examples.

References

M. Abt and W.J. Welch. Fisher information and maximum-likelihood estimation ofcovariance parameters in gaussian stochastic processes. The Canadian Journal ofStatistics, 26:127–137, 1998.

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U.N. Brimkulov, G.K. Krug, and V.L. Savanov. Numerical construction of exact exper-imental designs when the measurements are correlated. Zavodskaya Laboratoria, 36:435–442, 1980.

R.D. Cook and L.A. Thibodeau. Marginally restricted d-optimal designs. Journal ofthe American Statistical Association, 75:366–371, 1980.

N. Cressie. Statistics for spatial data. Wiley, New York, 1993.

M.N.L. Huang and M.C. Hsu. Marginally restricted linear-optimal designs. Journal ofStatistical Planning and Inference, 35:251–266, 1993.

J. Lopez-Fidalgo and S. Garcet-Rodrıguez. Optimal experimental designs when someindepedent variables are not subject to control. Journal of the American StatisticalAssociation, 99:1190–1199, 2004.

C.J. Nachtsheim. On the design experiments in the presence of fix covariates. Journalof Statistical Planning and Inference, 22:203–212, 1989.

D. Ucinski and A.C. Atkinson. Experimental design for time-dependent models withcorrelated observations. Studies in Nonlineal Dynamics & Econometrics, 8, 2004.

Optimal experimental designs for Cox Regression

JESUS LOPEZ-FIDALGOjesus.lopezfidalgo@uclm.esUniversity of Castilla-La Mancha, Spain

and

MARIA JESUS RIVAS-LOPEZ?

chusrl@usal.esUniversity of Salamanca, Spain

Under the Cox regression framework optimal experimental designs may be found whensome explanatory variables are under the control of the experimenter. Here the failuretime is modelized according to a probability distribution depending on some explanatoryvariables through a linear model. At the end of the study some units will have not failedand thus the time records will be censored. To deal with this problem a sequentialdesign may be used each time a new unit enters the study taking into account whathas happened until that moment. In this work a different approach is considered anda generic conditional design will be computed at the beginning of the study for anypossible given time of debut.

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The period of the study will be the interval [0, T ]. A particular experimental unit i(i = 1, . . . , n) will arrive randomly at time Ii. Then, ci = T − Ii will be the maximumtime the experimental unit i can be in the study. Since at the moment of designing theexperiment the times Ii are not known, a uniform distribution might be assumed forthese times.A simple example is considered to illustrate the procedure. Let z ∈ {0, 1} be theexplanatory variable under the control of the experimenter. For instance, it may be thecase of selecting one of two possible treatments to be assigned to a patient.An exponential distribution will be considered for the failure time. This distributionwill depend on a controllable variable through a linear model: t ≡ E(α + βz), where αand β are unknown parameters to be estimated such that α + βz > 0, z ∈ {0, 1}.Under this particular framework the optimal design approach turns to be equivalentto the theory of marginally restricted (MR) optimality given by Cook and Thibodeau(1980) for D–optimality, lately extended, e.g. by Lopez Fidalgo and Garcet-Rodrıguez(2004) for other criteria and situations.Let ξ1(c) be the marginal distribution of the maximum possible time c a experimentalunit can be in the study. And let p(c) be the conditional probability of z = 1 given c.The objective will be to find a function 0 ≤ p(c) ≤ 1, c ∈ [0, T ] such that the D-criterionis optimized. This function will provide an optimal conditional design to be applied inpractice given a particular value of c.

References

R.D. Cook and L.A. Thibodeau. Marginally restricted d–optimal designs. J. Am. Stat.Assoc., 75(370):366–371, 1980.

J. Lopez Fidalgo and S. Garcet-Rodrıguez. Optimal experimental designs when someindependent variables are not subject to control. J. American Statistical Association,99(468):1190–1199, 2004.

D–Optimal Designs for Regression Models withLength-Biased Poisson Response

ISABEL ORTIZ , CARMELO RODRIGUEZ and IGNACIO MARTINEZiortiz@ual.es, crt@ual.es, ijmartin@ual.esUniversidad de Almerıa, Spain

This paper is concerned with the search for locally optimal designs when the obser-vations of the response variable arise from a weighted distribution in an exponential

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family. The expression for the information matrices for length-biased distributions froman exponential family are obtained. Locally D–optimal designs are derived for regres-sion models whose response variable follows a weighted Poisson distribution. Two linkfunctions are considered for these models.

Determining the Size of Experiments for theOne-way ANOVA Model I for Ordered CategoricalData

DIETER RASCHdieter.rasch@boku.ac.atUniversity of Natural Resources and Applied Life Sciences Vienna, Austria

and

MARIE SIMECKOVA?

simeckova.marie@vuzv.czInstitute of Animal Science Prague - Uhrıneves, Czechia

We present a method of sample size determination for the one-way ANOVA modelwith a fixed factor and categorical data. The null hypothesis to be tested is that thedistribution of a random variable y in all a levels is the same. The method is based onthe relative effect (Brunner and Munzel (2002)) between the two extreme distributionsp = P (ymin < ymax) + 1/2 · P (ymin = ymax) =

∫FmindFmax and on the results for

determining the size of experiments as discussed in Herrendorfer et al. (1997).For fixed type-I-risk α = 0.05 and different numbers a of levels, relative effect size δ/σ,relative effect p, number of categories r of the response variable and power in [0.60, 0.95],the required sample size for the Kruskal – Wallis test can be calculated by our formula:

n(β) = 3.054 · n0(β)− 47.737 · δ

σ+ 51.288 · p2 + 82.050 · 1

r+

+2.336 · n0(β) · δ

σ− 7.428 · n0(β) · p2 − 0.535 · n0(β) · 1

r+

+29.708 · δ

σ· p2 + 56.102 · δ

σ· 1

r− 223.770 · p2 · 1

r.

References

E. Brunner and U. Munzel. Nichtparametrische Datenanalyse - unverbundene Stich-proben. Springer, Berlin, 2002.

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G. Herrendorfer, D. Rasch, K. Schmidt, and M. Wang. Determination of the size of anexperiment for the F-test in the analysis of variance – mixed model. In Wegman, E.J. and Azen, P. A.: Computing Science and Statistics, volume 29, 2, pages 547–550,Pasadena, February 1997.

Applications of Optimum Designs to theCharacterization of Adsorption Isotherms

LICESIO J. RODRIGUEZ-ARAGON and JESUS LOPEZ-FIDALGOL.RodriguezAragon@uclm.es, Jesus.LopezFidalgo@uclm.esUniversidad de Castilla-La Mancha, Spain

Adsorption phenomena are described using the relationship between the equilibriumpressure of the gas and the amount adsorbed at constat temperature, known as adsorp-tion isotherm. The Brunauer-Emmett-Teller (BET) model and the extension known asGuggenheim-Anderson-de Boer (GAB) model are widely used.The modeling of the adsorption phenomena in many chemical and industrial processesis proved to be of great interest. Consequently, a correct selection of the isotherm modeland a correct estimation of the parameters are crucial tasks.The first objective to characterize the adsorption phenomena is to choose which of themodels will best fit to the data. T−optimum designs have been obtained to discriminatebetween both models. Once the model has been selected the correct estimation of theparameters is crucial. The D− and c− optimality criteria are used in this work.The optimum designs are tools for the experimenter allowing to measure the efficiencyof any experimental design proposed by comparing it to the optimum.

Optimal Designs for a Modified Exponential Model

JUAN M. RODRIGUEZ-DIAZ? and MARIA TERESA SANTOS-MARTINjuanmrod@usal.es, maysam@usal.esUniversity of Salamanca, Spain

The Arrhenius equation is widely accepted as the right tool to describe the influence oftemperature on the rates of chemical processes. The model is equivalent to the well–known exponential model. Optimal designs for this have been already computed, spe-cially in Han and Chaloner (2003) for independent and normally-distributed errors withconstant variance and in Rodrıguez-Torreblanca and Rodrıguez Dıaz (2007) for differentvariance structures. Also optimal and compound designs specifically for the Arrhenius

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equation can be found in Rodrıguez-Aragon and Lopez-Fidalgo (2005). However, forthe analysis of more precise rate-temperature data, particularly in studies covering awide temperature range, it is very often to use the Modified-Arrhenius (MA) model. Inthis paper, optimal designs for the MA model will be computed through the study ofthe equivalent modification of the exponential model.

References

C. Han and K. Chaloner. D- and c-optimal designs for exponential regression modelsused in viral dynamics and other applications. Journal of Statistical Planning andinference, 115:585–601, 2003.

L.J. Rodrıguez-Aragon and J. Lopez-Fidalgo. Optimal designs for the arrhenius equa-tion. Chemometrics and Intelligent Laboratory Systems, 77:131–138, 2005.

C. Rodrıguez-Torreblanca and J.M. Rodrıguez Dıaz. Locally d- and c-optimal designsfor poisson and negative binomial regression models. Metrika (in press), 2007.

Mixed Poisson fields as models for consumerpurchase events

VIPPAL SAVANI? and ANATOLY ZHIGLJAVSKYSavaniV@cf.ac.uk, ZhigljavskyAA@cf.ac.ukCardiff University, UK

Mixed Poisson processes have been widely used as natural models for events occurringin continuous or discrete time in many different areas including accident proneness, ac-cidents and sickness, market research, risk theory and clinical trials. In this presentationwe consider application of the mixed Poisson process and mixed Poisson field models tothe purchase events in market research.One of our results is the derivation of the joint asymptotic distributions of statisticsof homogeneous mixed Poisson processes, including parameter estimators, computed indifferent time intervals from data generated by mixed Poisson processes. These distri-butions allow, in particular, to test hypotheses for assessing goodness of fit of the mixedPoisson model.We show how to transform non-homogeneous mixed Poisson processes to the homoge-neous processes which allows the removal of seasonal effects. All discussion is illustratedon real data examples.

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QstatLab: software for statistical process controland robust engineering

IVAN N. VUCHKOV?

qstat@dir.bgUniversity of Chemical Technology & Metallurgy, Bulgaria

A software for quality improvement is presented. The main difference with respect to theexisting statistical software products is that it contains programs for model based qualityengineering. They make it possible to create models of performance characteristics inthe cases when there are errors in the factors, for products with errors in factors andexternal noises and for mechanistic models with errors in factors and external noises.Quality improvement based on simulations of errors is also possible. These methodsare combined with a set of programs for multicriterion optimization with constraintsand for finding Pareto optimal solutions. Sequences of optimization methods are alsoavailable. The software contains also most of the traditional statistical methods forquality improvement.QstatLab is targeted to users with basic knowledge of statistical methods.

The Fisher Information in Nonlinear ExperimentalDesign

EMANUEL WINTERFORS?

winterfors@ann.jussieu.frUniversite Pierre et Marie Curie, France

A novel way of defining the Fisher information is proposed, which is independent ofchoice of coordinates. Its use in experimental design for nonlinear problems is investi-gated and relations for the expected gain in Fisher information are derived that parallelswell-known results for the expected gain in Shannon information Lindley (1956); Sebas-tiani and Wynn (2000). Relations to the expected variance of the experimental outcomeare also derived. Comparisons are also made to the conventional use of Fisher infor-mation in experimental design by approximate methods based on local linearisation,illustrated by a simple example.

References

D. V. Lindley. On a measure of the information provided by an experiment. Ann. Math.Statist., 27:986–1005, 1956.

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Paola Sebastiani and Henry P. Wynn. Maximum entropy sampling and optimal Bayesianexperimental design. J. R. Stat. Soc. Ser. B Stat. Methodol., 62(1):145–157, 2000.ISSN 1369-7412.

Bayesian information-based learning

HENRY P. WYNNh.wynn@lse.ac.ukLondon School of Economics, UK

In the context of Bayesian learning where there is a prior distribution π(θ) on theparameter θ and a sampling distribution f(x, θ), the prior expectation of the posteriorShannon information is EXEθ|X log π(θ|X) = EX,θ log π(θ|x). It is well known that thisquantity is greater than the Shannon information for the prior Eθ log π(θ), although forspecial cases the actual Shannon information may decrease. This is a special case ofa more general result that includes Shannon information and all Renyi α-information.As a statement about Bayesian experimental design this says that, in a general sense,we always expect to learn but there are cases where we do not learn. The questionof whether information increases, that is we learn, is closely related to the theory ofcontinuous majorization based on decreasing rearrangements.

Efficient Conjoint Choice Designs for Mixed LogitModels

JIE YU?, MARTINA VANDEBROEKJie.Yu@econ.kuleuven.be, Martina.Vandebroek@econ.kuleuven.beKatholieke Universiteit Leuven, Belgium.

PETER GOOSPeter.Goos@ua.ac.beUniversiteit Antwerpen, Belgium.

The authors propose a fast and efficient algorithm for constructing D-optimal conjointchoice designs for mixed logit models. With this new algorithm, the construction of semi-Bayesian D-optimal mixed logit designs and designs with large numbers of attributes andattribute levels becomes practically feasible. The results from the comparison of eightdesigns (ranging from the simple locally D-optimal multinomial logit design and thenearly orthogonal design generated by Sawtooth (CBC) to the complex semi-Bayesian

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mixed logit design) across wide ranges of parameter values show that the semi-Bayesianmixed logit approach outperforms the competing designs not only in terms of estimationefficiency but also in terms of predicting choice probabilities. In particular, it was foundthat semi-Bayesian mixed logit designs constructed with large heterogeneity parametersare most robust against the misspecification of the values for the mean of the individual-level coefficients for making precise estimations and predictions.

Optimal designs for Gaussian random fields withexponential correlation structure

MAROUSSA ZAGORAIOU? and ALESSANDRO BALDI ANTOGNINIzagoraiou@stat.unibo.it, baldi@stat.unibo.itUniversity of Bologna, Italy

In this paper we study the optimal design problem for a random field regression modelof the form Y (x) = β + Z(x), where x lies in a compact subset X ⊂ R, β ∈ R and Z(x)is a zero-mean Gaussian process with constant variance σ2 and exponential correlationstructure given by

Corr (Z(x); Z(x′)) = exp(−θ|x− x′|), θ ∈ R+.

These kind of models are traditionally used in spatial statistics and have become verypopular in the computer experiments literature (see Sacks et al. (1989) and Bursztynand Steinberg (2006)).Without loss of generality we assume that X = [0; 1], so the design problem consists inchoosing n sites x1, . . . , xn ∈ [0, 1] with xi 6= xj (i.e. without replications) in order tomaximize the information on the parameters of interest.When the maximum likelihood method is used, Pazman (2004) has shown that undermild assumptions the MLE’s (β, θ) are approximately unbiased, uncorrelated, with co-variance given by the inverse of the Fisher information matrix (see for instance Zhuand Stein (2005)). Following this approach, we study the optimal designs when theinferential purpose is only one of the parameters, namely either β or θ. Furthermore,we propose a multiple-objective design approach (see Wong (1999)) when the interest isfocused on both parameters.

References

D. Bursztyn and D.M. Steinberg. Comparisons of designs for computer experiments.Journal of Statistical Planning and Inference, 136:1103–1119, 2006.

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A. Pazman. Correlated optimum design with parametrized covariance function: justifi-cation of the fisher information matrix and of the method of virtual noise. ResearchReport Series of the Department of Statistics and Mathematics, WirtschaftsuniversitatWien, 5, 2004.

J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn. Design and analysis of computerexperiments. Statistical Science, 4:409–423, 1989.

W.K. Wong. Recent advances in multiple-objective design strategies. Statistica Neer-landica, 53:257–276, 1999.

Z. Zhu and M.L. Stein. Spatial sampling design for parameter estimation of the covari-ance function. Journal of Statistical Planning and Inference, 134:583–603, 2005.

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68

SOCIAL EVENTS

Social Events mODa8

ALMAGRO

Almagro comes from the arabic word Almagreb meaning red clay. It is a land of Knights,where you can stroll through expecting to meet the ghosts and heroes mentioned byCervantes in the words of Don Quixote and Sancho Panza.Almagro is the center of “El Campo de Calatrava” a large flat land assigned to theCalatrava Knights after recovering its property from the moors who upholded it forover six hundred years. Within its walls many brave people were bred such as Diego deAlmagro the Spanish Conquistador who participated in the Spanish conquest of Peruand is credited as the first European discoverer of Chile.The Emperor Charles V chose Almagro as the base for transactions between the differentcountries of his empire (Northern Europe, America, Italy, Greece, Northern Africa andSpain). The settlement of Flemish bankers and their dynasties show the present rem-iniscences of Flemish Fugger houses with its typical stained glassed balconies, Hollandtapestries and embroideries.

Many cultural activities are currently present in this smalltown: the Theater Court (El Corral de Comedias) is aXVII century Theater, where the first Spanish Comedies wereheld, and is preserved with its original structure in parallelwith the Shakespearean theater The Globe. It was built asa Comedy Theater and an inn. It is still used for dramaticperformances.The National Festival of Classical Theater takes place inAlmagro every year in July and offers performances of classic

plays by Spanish and international dramatists. The New Theater of Almagro (Museodel Teatro) deserves a visit as well as the Costumes Museum attached to it. The visitis free for participants after showing the mODa badge.

Staying In Almagro

As you have probably noticed Almagro is a little town of no more than 8500 inhabitants.Consequently everything is within 10 minutes walk. There are some places marked inthe map so that you feel at home during your stay in Almagro.mODa refers to the conference hall and the building where some of you are lodged.The building, known as the Palace of the Earls of Valdeparaıso, was built in the XVIIIcentury and it is now owned by the county of Ciudad Real, which dedicates it to culturalactivities.Posada de Almagro: Where some of you are lodged, corresponds to the architecturaltype of a traditional lodge. Stocking rooms, cavalries, brewing wine and oil faciliteshave been remodeled into a restaurant and hotel.Hotel Retiro del Maestre: A modern hotel built following the mansion structure ofthe area. With a beautiful patio, balconies, that collaborates to maintain the Mancha

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traditional taste and architecture.Hostal San Bartolome: A rural mansion adapted into a hotel with a distinct stylefor each room in which the rural feeling still remains.

Parador: The Parador of Almagro is part of the National Paradores run by the StateTourist Office. All the buildings officially run as Paradores are historical buildingsoffered to the public as hotels. This Parador is a landmark in Almagro as it was initiallya monastery founded in the XVII by Jeronimo de Avila and his wife. The church andthe cloister (Patio del Laurel) belong to the original building and legend says thatpeople can still hear voices corresponding to visiting ghosts. Meals will be served in thebuilding.Hospederıa de Almagro: In the Convent of the Asuncion (Assumption) built in theXVII century by Calatravan knights and latterly turned into a Dominican Convent hasa magnificent Cloister with beautiful columns from Carrara (Italy). Part of it is hasbeen turned into a restaurant where the Conference dinner will take place.

De Canas Y Tapas Por Almagro

A “cana” pronounced (cagna) consists of a small drink of draught beer that you drinkusually accompanied by a small bite “tapa”.

As basic information for walking around Almagro we will point out three areas whereyou can have snacks, coffee and dinner. If you want to follow the Spanish trend, at least

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for the days ahead, we suggest to have some beer, wine or soft drinks at some of thebars and pubs in Almagro. In these places each drink is accompanied by a “tapa” theprice of which is usually included and varies between 1 and 2 e. If you want to haveyour drinks at a terrace enjoying the evening atmosphere a small charge is included.

Instead of a full meal and specially in the companyof several friends you can enjoy “raciones”, a dish toshared. Typical “raciones” that you will see announcedover the bar or in menu cards are: Jamon, Chorizo,Lomo (which are typical products from the Iberian Pig),Queso curado and Queso en aceite (sheep cheesetypically preserved in olive oil), Migas, Asadillo, Du-elos y Quebrantos (typical dishes from La Manchaquoted in the Quixote), Calamares (Calamari), Gam-

bas (Shrimps) and small Fishes fried in olive oil. The price of these “raciones” variesbetween 8-15 e and we would suggest three “raciones” to be shared among four people.A typical product form Almagro that you will see at bars and shops are the Berenjenade Almagro, aubergine or eggplant served as pickle. Wine and Olive oil are alsorepresentative of the area.At the Plaza Mayor (Main Square) you may find several bars as “La Columna delZurdo” (1), “Tabernilla Las Nieves” (2), “Plaza Mayor” with a restaurant in the firstfloor overlooking the main square (3), “El Gordo” famous for its tapas (4).Nearby the Hospederıa you can also find “El Pollo” (5), “Pizzeria Buenos Aires” withhomemade pizzas (6) and “Bar Carmelo” (7).And opposite the Parador, “Bar San Francisco” and “La Muralla” (8) are also advisableplaces.Close to the main square you can reach several banks, Banco Santander, Caja Castilla-La Mancha and Caja Rural with opening times between 9 and 14.

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TOLEDO

Toledo is a city located in central Spain, about 100 kilometers south of Madrid. It isthe capital of the province of Toledo and of the autonomous community of Castile-LaMancha. It was declared a World Heritage Site by UNESCO in 1986, due to its extensivecultural and monumental heritage as one of the former capitals of the Spanish Empireand place of coexistence of Christian, Jewish and Moorish cultures. Many famous peopleand artists were born or lived in this city, including Garcilaso de la Vega, Alfonso Xand El Greco, and it was the place of important historic events such as the VisigothicCouncils of Toledo. As of 2005, the city has a population of 75,578 and an area of 232.1square kilometers (89.59 square miles).

History

As encountered by the Romans, the city called Toletum was the capital of the Car-petani. It was incorporated into the Roman province of Hispania Tarraconensis. It satat a strategic location along the Tagus River and on the road from Emerita (modernMerida) to Caesaraugusta (modern Zaragoza), and connected also by another road withLaminium. It was a very strong town, though only of moderate size, and famed for itsmanufacture of arms and steel-ware. According to an old Spanish tradition, Toledo wasfounded in the year 540 BC by Jewish colonists, who named it Toledoch, that is, motherof people, whence one might perhaps infer a Phoenician settlement.Toledo later served as the capital city of Visigothic Spain, beginning with Liuvigild(Leovigild), and was the capital until the Moors conquered Iberia in the 8th century.Under the Caliphate of Cordoba, Toledo enjoyed a golden age. This extensive period isknown as La Convivencia, i.e. the co-existence of Jews, Christians, and Muslims. UnderArab rule, Toledo was called Tulaytulah.On May 25, 1085 Alfonso VI of Castile took Toledo and established direct personalcontrol over the Moorish city from which he had been exacting tribute. This was thefirst concrete step taken by the combined kingdom of Leon-Castile in the Reconquistaby Christian forces.Toledo was famed for its production of steel and especially of swords and the city isstill a center for the manufacture of knives and other steel implements. When Philip

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II moved the royal court from Toledo to Madrid in 1561, the old city went into a slowdecline from which it never recovered.

Toledo’s Alcazar became renowned in the 19th and 20th centuries as a military academy.At the outbreak of the Spanish Civil War in 1936 its garrison was famously besieged byRepublican forces.

Arts And Culture

Toledo saw its glory days in the era of Islamic Caliphate when it was a beautiful com-bination of art and science. Perhaps the most prominent masterpiece of art was the“waterlocks of Toledo”. Famous historian P. de Gayangos writes an example of such amerger of science and arts as:

“The Muslim scientists of this age were unrivaled in the world. Perhaps among theirgreatest feats were the famous waterlocks of Toledo.”

The old city is located on a mountaintop, surrounded on three sides by a bend in theTagus River, and contains many historical sites, including the Alczar, the cathedral (theprimate church of Spain), and the Zocodover, a central marketplace.

From the 5th century to the 16th century about thirty churchsynods were held at Toledo. The earliest, directed againstPriscillian, assembled in 400. At the synod of 589 the Visig-othic King Reccared declared his conversion from Arianism;the synod of 633 decreed uniformity of liturgy throughoutthe Visigothic kingdom and took stringent measures againstbaptized Jews who had relapsed into their former faith. Thecouncil of 681 assured to the archbishop of Toledo the pri-macy of Spain.

As nearly one hundred early canons of Toledo found a placein the Decretum Gratiani, they exerted an important influ-ence on the development of ecclesiastical law. The synod of1565-1566 concerned itself with the execution of the decreesof the Council of Trent; and the last council held at Toledo,

1582-1583, was guided in detail by Philip II.

Toledo was famed for religious tolerance and had large communities of Muslims and Jewsuntil they were expelled from Spain in 1492 and 1604; the city therefore has importantreligious monuments like the Synagogue of Santa Mara la Blanca, the Synagogue of ElTransito, and the Mosque of Cristo de la Luz.

In the 13th century, Toledo was a major cultural center under the guidance of AlfonsoX, called “El Sabio” (“the Wise”) for his love of learning. The program of translations,begun under Archbishop Raymond of Toledo, continued to bring vast stores of knowledgeto Europe by rendering great academic and philosophical works in Arabic and Hebrew

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into Latin.

The cathedral of Toledo (Catedral de Toledo) was modeled after the Bourges Cathedralthough it also combines some characteristics of the Mudejar style. It is remarkable forits incorporation of light and features the Baroque altar called El Transparente, severalstories high, with fantastic figures of stucco, painting, bronze castings, and multiplecolors of marble, a masterpiece of medieval mixed media by Narciso Tom topped by thedaily effect for just a few minutes of a shaft of light. It is from this feature that thecathedral derives its name.Toledo was home to El Greco for the latter part of his life, and is thesubject of some of his most famous paintings, including The Burialof the Count of Orgaz, exhibited in the Church of Santo Tome.Additionally, the city was renowned throughout the middle ages andinto the present day as an important center for the production ofswords and other bladed instruments.

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76

Index

Allenby, G., 33Amo-Salas, M., 50Anisimov, V.V., 21Atkinson, A.C., 26

Bailey, R., 43Baldi Antognini, A., 53, 66Basso, D., 43Benda, N., 45Biedermann, S., 40Biswas, A., 23Bogacka, B., 26, 29Bonnini, S., 42

Curtis, A., 30

Dean, A., 33Dette, H., 40Dorta-Guerra, R., 50Downing, D., 21

Fathy, Y., 35Fedorov, V.V., 21, 22Flournoy, N., 24, 25

Garcet-Rodrıguez, S., 51Garroi, J., 37Giancristofaro, R., 42Ginebra, J., 50Giovagnoli, A., 53Goegebeur, Y., 54Gonzalez-Davila, E., 50Goos, P., 31, 32, 37, 54, 65Graßhoff, U., 45Großmann, H., 45Gumprecht, D., 39

Haines, L.M., 27Hardwick, J., 22Harman, R., 49Haycroft, R., 54Hilgers, R.D., 44, 55

Hoffmann, P., 40Holling, H., 45

Ivanova, A., 20

Jurık, T., 49

Kabera, M.G., 27Kunert, J., 43

Lopez, V., 56Lopez-Fidalgo, J., 32, 34, 50, 51, 58, 59, 62Lane, P, 48Laycock, P.J., 32Leonov, S.L., 21Li,W., 47Liu, Q., 33

Muller, C., 35Muller, W.G., 39Mandal, S., 23Martınez, I., 60Martın-Martın, R., 58Maruri-Aguilar, H., 42May, C., 24Melas, V., 28Moler, J.A., 25

Ndlovu, P., 27Nguyen, T., 46

O’Brien, T.E., 27Ortiz, I., 60

Patan, M., 29Pepelyshev, A., 39Pesarin, F., 42, 43Ponce de Leon , A., 28Pronzato, L., 57Pazman, A., 57

Ramos, R., 56Rasch, D., 61

77

Riccomagno, E., 42Rivas-Lopez, M.J., 59Rodrıguez-Aragon, L.J., 62Rodrıguez-Dıaz, J.M., 39, 50, 62Rodrıguez, C., 60Rodrigues Pinto, E., 28Rosenberger, W. F., 20

Sorensen, K., 37Salmaso, L., 43Santos-Martın, M.T., 62Savani, V., 63Schmelter, T., 45Schwabe, R., 45Simeckova, M., 61Spock, G., 36Stanzel, S., 44Stehlık, M., 37, 58Stout, Q.F., 22Sverdlov, O., 20

Tommasi, C., 40Torsney, B., 46Trnovska, M., 49Tsai, K., 47

Vandebroek, M., 32, 54, 65Vermeulen, B., 32Villarroel, J., 34Vuchkov, I.N., 64

Winterfors, E., 30, 64Wu, Y., 22, 48Wynn, H.P., 65

Ye, K., 47Yu, J., 65

Zagoraiou, M., 66Zhigljavsky, A., 46, 54, 63

LIST OF PARTICIPANTS

List of participants mODa8

LIST OF PARTICIPANTS

Miguel Adan Miguel.Adan@uclm.esMariano Amo-Salas Mariano.Amo@uclm.esVladimir V. Anisimov Vladimir.V.Anisimov@gsk.comAnthony C. Atkinson a.c.atkinson@lse.ac.ukRosemary Bailey r.a.bailey@qmul.ac.ukAlessandro Baldi Antognini baldi@stat.unibo.itDario Basso dario@stat.unipd.itNorbert Benda norbert.benda@novartis.comStefanie Biedermann S.Biedermann@soton.ac.ukAtanu Biswas atanu@isical.ac.inBarbara Bogacka B.Bogacka@qmul.ac.ukStefano Bonnini bnnsfn@unife.itClive Bowman clive.e.bowman@gsk.comChing-Shui Cheng cheng@stat.berkeley.eduAngela Dean dean.9@osu.eduRoberto Dorta-Guerra rodorta@ull.esDarryl J. Downing darryl.j.downing@gsk.comValerii V. Fedorov Valeri.V.Fedorov@gsk.comMercedes Fernandez-Guerrero mercedes.fernandez@uclm.esNancy Flournoy flournoyn@missouri.eduSandra Garcet Rodrıguez sandra garcet@usal.esJean-Jacques Garroi Jean-Jacques.Garroi@ua.ac.beAlessandra Giovagnoli alessandra.giovagnoli@unibo.itPeter Goos peter.goos@ua.ac.beHeiko Großmann h.grossmann@qmul.ac.ukPeter Hackl Peter.Hackl@statistik.gv.atLinda M. Haines lhaines@stats.uct.ac.zaRadoslav Harman harman@fmph.uniba.skRebecca Haycroft HaycroftRJ@cf.ac.ukRalf-Dieter Hilgers rdhilgers@ukaachen.deAnastasia Ivanova aivanova@bios.unc.eduJoachim Kunert joachim.kunert@udo.eduPeter Lane peter.w.lane@gsk.comPatrick J. Laycock pjlaycock@manchester.ac.ukSergei L. Leonov Sergei.2.Leonov@gsk.comVıctor Lopez Rıos vilopez@cimat.mxJesus Lopez-Fidalgo jesus.lopezfidalgo@uclm.esFrank Mannino frank.v.mannino@gsk.comIgnacio Martınez Lopez ijmartin@ual.es

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Raul Martın-Martın Raul.MMartin@uclm.esHugo Maruri-Aguilar H.Maruri-Aguilar@lse.ac.ukCaterina May cmay@mat.unimi.itViatcheslav Melas v.melas@pobox.spbu.ruJose A. Moler jmoler@unavarra.esChristine Mueller cmueller@mathematik.uni-kassel.deWerner G. Muller werner.mueller@jku.atIsabel Marıa Ortiz-Rodrıguez iortiz@ual.esMaciej Patan M.Patan@issi.uz.zgora.plAndrey Pepelyshev andrey@ap7236.spb.eduFortunato Pesarin fortunato.pesarin@unipd.itAntonio Ponce de Leon ponce@ims.uerj.brDieter Rasch DAMK.Rasch@t-online.deEva Riccomagno Eva.Riccomagno@polito.itMarıa Jesus Rivas-Lopez chusrl@usal.esEdmilson Rodrigues-Pinto edmilson@famat.ufu.brCarmelo Rodrıguez-Torreblanca crt@ual.esLicesio J. Rodrıguez-Aragon l.rodriguezaragon@uclm.esJuan M. Rodrıguez-Dıaz juanmrod@usal.esJames Roger james.h.roger@gsk.comWilliam F. Rosenberger wrosenbe@gmu.eduKatrin Roth katrin.roth@schering.deM Teresa Santos-Martın maysam@usal.esVippal Savani savaniv@cardiff.ac.ukThomas Schmelter thomas.schmelter@schering.deRainer Schwabe rainer.schwabe@mathematik.uni-magdeburg.deMarie Simeckova simeckova.marie@vuzv.czGunter Spoeck gunter.spoeck@uni-klu.ac.atSven Stanzel sstanzel@medfak.rwth-aachen.deMilan Stehlık Milan.Stehlik@jku.atQuentin F. Stout qstout@umich.eduChiara Tommasi chiara.tommasi@unimi.itBen Torsney bent@stats.gla.ac.ukPaula Camelia Trandafir camelia.trandafir@gmail.comMartina Vandebroek martina.vandebroek@econ.kuleuven.beBart Vermeulen bart.vermeulen@econ.kuleuven.beJavier Villarroel Javier@usal.esIvan Vuchkov qstat@dir.bgEmanuel Winterfors winterfors@ann.jussieu.frYuehui Wu yuehui.2.wu@gsk.com

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Henry P. Wynn h.wynn@lse.ac.ukKenny Ye kye@aecom.yu.eduJie Yu jie.yu@econ.kuleuven.beMaroussa Zagoraiou zagoraiou@stat.unibo.itAnatoly Zhigljavsky ZhigljavskyAA@cf.ac.uk

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Diputación Provincial de Ciudad Real

Universidad de Castilla-La Mancha

Vicerrectorado del Campus de Ciudad Real y Cooperación Cultural GlaxoSmithKline

Escuela Superior de Informática Ayuntamiento de Almagro E.T.S. Ingenieros

Industriales

Universidad de Almería

Caja Castilla-La Mancha Ministerio de

Educación y Ciencia