Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

Wang, Lin; Xiao, Qian; Xu, Hongquan

doi:10.1214/17-aos1674

Cited by 47 publications

(33 citation statements)

References 30 publications

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“…Orthogonality [Owen (1994), Tang (1998), Ye (1998)] and maximin distance criterion [Johnson, Moore and Ylvisaker (1990), Zhou and Xu (2014)] are two most commonly used design criteria. A number of authors have constructed orthogonal and maximin LHDs; see Lin and Tang (2015) for an excellent review, as well as Sun and Tang (2017), Xu (2017, 2018) and Wang, Xiao and Xu (2018) for some recent works. However, as Joseph and Hung (2008) and Xiao and Xu (2018) pointed out, orthogonal LHDs often do not have maximin distance and maximin distance designs are often not orthogonal, except for some specific cases [Wang, Yang and Xu (2018)].…”

Section: Introductionmentioning

confidence: 99%

Uniform projection designs

Sun¹,

Wang²,

Xu³

2019

Ann. Statist.

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Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-filling properties in terms of distance, uniformity and orthogonality. We show that the new criterion is a function of the pairwise L 1 -distances between the rows, so that the new criterion can be computed at no more cost than a design criterion that ignores projection properties. We develop some theoretical results and show that maximin L 1 -equidistant designs are uniform projection designs. In addition, a class of asymptotically optimal uniform projection designs based on good lattice point sets are constructed. We further illustrate an application of uniform projection designs via a multidrug combination experiment.

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Section: Introductionmentioning

confidence: 99%

Uniform projection designs

Sun¹,

Wang²,

Xu³

2019

Ann. Statist.

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“…Due to the complexity of underlying biological systems, a systematic quantification of effects for multiple drugs is challenging, and thus, various models should be explored for such experiments. In such situations, space‐filling designs are ideal due to their robustness . Maximin distance designs are ideal for kriging models, as any unobserved point will not be too far from observed design points and thus the prediction error will not be too big.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In such situations, space-filling designs are ideal due to their robustness. [20][21][22][23][24] Maximin distance designs are ideal for kriging models, as any unobserved point will not be too far from observed design points and thus the prediction error will not be too big. An interesting topic for the future research is how space-filling designs, especially maximin distance designs, perform under kriging models in drug combination studies.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Application of kriging models for a drug combination experiment on lung cancer

Xiao

Wang

2018

Statistics in Medicine

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Combinatorial drugs have been widely applied in disease treatment, especially chemotherapy for cancer, due to its improved efficacy and reduced toxicity compared with individual drugs. The study of combinatorial drugs requires efficient experimental designs and proper follow-up statistical modeling techniques. Linear and nonlinear models are often used in the response surface modeling for such experiments. We propose the use of kriging models to better depict the response surfaces of combinatorial drugs. We illustrate our method via a drug combination experiment on lung cancer and further show how proper experimental designs can reduce the necessary run size. We demonstrate that only 27 runs are needed to predict all 512 runs in the original experiment and achieve better precision than existing analyses.

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“…Note that linearly permuted regular designs can be still considered as regular because they are just cosets of regular designs and share the same defining relationship. We consider a nonlinear level permutation via the Williams transformation, which was first used by Williams (1949) to construct balanced Latin square designs, followed by Butler (2001) and Wang et al (2018b) to construct orthogonal or maximin LHDs. Our purpose is different from theirs.…”

Section: Introductionmentioning

confidence: 99%

A Class of Multilevel Nonregular Designs for Studying Quantitative Factors

Wang¹,

Xu²

2022

STAT SINICA

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Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the construction of nonregular designs focuses on two-level designs. We provide a novel class of multilevel nonregular designs by permuting levels of regular designs. We develop a theory illustrating how levels can be permuted without computer search and accordingly propose a sequential method for constructing nonregular designs. Compared to regular designs, these nonregular designs can provide more accurate estimations on factorial effects and more efficient screening for experiments with quantitative factors. We further explore the space-filling property of the obtained designs and demonstrate their superiority.

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Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

Cited by 47 publications

References 30 publications

Uniform projection designs

Uniform projection designs

Application of kriging models for a drug combination experiment on lung cancer

A Class of Multilevel Nonregular Designs for Studying Quantitative Factors

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