On efficient exact experimental designs for ordered treatments

Singh, Satya Prakash; Davidov, Ori

doi:10.1016/j.csda.2021.107305

Computational Statistics & Data Analysis

2021

DOI: 10.1016/j.csda.2021.107305

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On efficient exact experimental designs for ordered treatments

Satya Prakash Singh

Ori Davidov

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Cited by 3 publications

References 9 publications

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Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests

Duarte

Atkinson²,

Singh³

et al. 2022

Stat Papers

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We find experimental plans for hypothesis testing when a prior ordering of experimental groups or treatments is expected. Despite the practical interest of the topic, namely in dose finding, algorithms for systematically calculating good plans are still elusive. Here, we consider the Intersection-Union principle for constructing optimal experimental designs for testing hypotheses about ordered treatments. We propose an optimization-based formulation to handle the problem when the power of the test is to be maximized. This formulation yields a complex objective function which we handle with a surrogate-based optimizer. The algorithm proposed is demonstrated for several ordering relations. The relationship between designs maximizing power for the Intersection-Union Test (IUT) and optimality criteria used for linear regression models is analyzed; we demonstrate that IUT-based designs are well approximated by C-optimal designs and maximum entropy sampling designs while D A -optimal designs are equivalent to balanced designs. Theoretical and numerical results supporting these relations are presented.

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Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests

Duarte

Atkinson²,

Singh³

et al. 2022

Stat Papers

View full text Add to dashboard Cite

show abstract

Some design considerations for cluster randomized trials with binary responses

Singh

Pal

Singh

2021

Communications in Statistics - Theory and Methods

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Optimal designs for testing pairwise differences: A graph‐based game theoretic approach

Singh,

Davidov

2024

Scandinavian J Statistics

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In a variety of experimental settings there is an interest in comparing pairs–of–treatments. Such experiments usually address one of the following two scientific questions: (1) is there a difference within any of the selected pairs of treatments? or (2) is there a difference within all of the selected pairs of treatments? In this article, we propose max–min optimal designs for testing the above hypotheses using a graph‐based game theoretic approach. Some of the max–min designs obtained are well known, but not recognized as optimal, others are novel and provide an improvement over naive designs.

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On efficient exact experimental designs for ordered treatments

Cited by 3 publications

References 9 publications

Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests

Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests

Some design considerations for cluster randomized trials with binary responses

Optimal designs for testing pairwise differences: A graph‐based game theoretic approach

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