Strategies for Supersaturated Screening: Group Orthogonal and Constrained Var(s) Designs

Abstract

Despite the vast amount of literature on supersaturated designs (SSDs), there is a scant record of their use in practice. We contend this imbalance is due to conflicting recommendations regarding SSD use in the literature as well as the designs’ inabilities to meet practitioners’ analysis expectations. To address these issues, we first summarize practitioner concerns and expectations of SSDs as determined via an informal questionnaire. Next, we discuss and compare two recent SSDs that pair a design construction method with a particular analysis method. The choice of a design/analysis pairing is shown to depend on the screening objective. Group orthogonal SSDs, when paired with our new, modified analysis, are demonstrated to have high power even with many active factors. Constrained positive Var(s)-optimal designs, when paired with the Dantzig selector, are recommended when effect directions can be credibly specified in advance; this strategy reasonably controls Type I error rates while still identifying a high proportion of active factors.

KEYWORDS:

• Dantzig selector
• GO-SSD
• Orthogonality
• Power
• Sparsity
• Type I error

Supplementary Materials

Supplementary Materials 1.pdf File titled “Supplementary Materials 1” containing additional simulation results and full questionnaire analysis.

Copy of SSD questions.pdf Copy of questionnaire discussed in Section 2.designs-catalog-Var(s).zip Catalog of $\text{Var}(s+)$ designs for $5\le n\le 50$ with $n+1\le k\le 2n$.

Dantzig Function.R R code for Dantzig selector function with data-driven γ and profile plot.

GOSSD Screen.R R code for implementing the MaxPower analysis method for GO-SSD analysis.paper-designs.zip File containing all designs used in the article.

Acknowledgments

The authors would like to thank the associate editor and three reviewers for their careful comments and suggestions that greatly improved the content and presentation of this work.