Blocked Designs for Experiments With Correlated Non-Normal Response

Woods, David C.; Ven, Peter M. van de

doi:10.1198/tech.2011.09197

Cited by 36 publications

(39 citation statements)

References 24 publications

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“…Khuri, Mukherjee, Sinha, and Ghosh (2006) provided a systematic study of the optimal design problem in the GLM setup and recently there has been an upsurge in research in both theory and computation of optimal designs. Russell et al (2009), Majumdar (2008, 2009), Stufken (2009), Yang, Zhang, andHuang (2011), Stufken and Yang (2012) are some of the papers that developed theory, while Woods et al (2006), Steinberg (2006, 2008), Waterhouse et al (2008), Woods and van de Ven (2011) focused on developing efficient numerical techniques for obtaining optimal designs under generalized linear models. Our focus is on optimal designs for GLMs with qualitative factors.…”

Section: Introductionmentioning

confidence: 99%

Optimal designs for 2k factorial experiments with binary response

Yang¹,

Mandal²,

Majumdar³

2017

STAT SINICA

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Abstract:We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and k qualitative factors each at two levels. We obtain a characterization of locally D-optimal designs. We then develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained easily using our algorithm for locally D-optimal designs and are good surrogates for Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study robustness with respect to the assumed parameter values of locally D-optimal designs.Key words and phrases: D-optimality, EW D-optimal design, fractional factorial design, full factorial design, generalized linear model, uniform design.

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Section: Introductionmentioning

confidence: 99%

Optimal designs for 2k factorial experiments with binary response

Yang¹,

Mandal²,

Majumdar³

2017

STAT SINICA

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“…Experiments for the collection of data in batches or blocks are prevalent in applied science and technology in areas such as pharmacology (Mentré et al 1997), agriculture (Patterson and Hunter 1983) and aeronautics (Woods and van de ven 2011). When modelling data from such experiments, it is important to account for the correlation or dependence of observations collected in a given batch or a given block.…”

Section: Introductionmentioning

confidence: 99%

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

et al. 2015

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Motivated by the need to sequentially design experiments for the collection of data in batches or blocks, a new pseudo-marginal sequential Monte Carlo algorithm is proposed for random effects models where the likelihood is not analytic, and has to be approximated. This new algorithm is an extension of the idealised sequential Monte Carlo algorithm where we propose to unbiasedly approximate the likelihood to yield an efficient exact-approximate algorithm to perform inference and make decisions within Bayesian sequential design. We propose four approaches to unbiasedly approximate the likelihood: standard Monte Carlo integration; randomised quasi-Monte Carlo integration, Laplace importance sampling and a combination of Laplace importance sampling and randomised quasi-Monte Carlo. These four methods are compared in terms of the estimates of likelihood weights and in the selection of the optimal sequential designs in an important pharmacological study related to the treatment of critically ill patients. As the approaches consid-B J. M. McGree ered to approximate the likelihood can be computationally expensive, we exploit parallel computational architectures to ensure designs are derived in a timely manner.

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“…In Section 2, we introduce the statistical models we employ, including copulas, and develop design methods for blocked experiments. An illustrative comparison is made to previous design approaches based on GEEs using an example from the work of Woods and vande Ven . In Section 3, we demonstrate and assess our methods via application to the materials testing example.…”

Section: Introductionmentioning

confidence: 99%

Copula‐based robust optimal block designs

Rappold

Müller

Woods

2019

Appl Stoch Models Bus & Ind

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Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.

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Blocked Designs for Experiments With Correlated Non-Normal Response

Cited by 36 publications

References 24 publications

Optimal designs for 2k factorial experiments with binary response

Optimal designs for 2k factorial experiments with binary response

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

Copula‐based robust optimal block designs

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