Optimal Row–Column Designs in High-Throughput Screening Experiments

Saturated row–column designs are studied to eliminate row and column effects in primary high-throughput screening experiments. All paired comparisons of treatments in the designs recommended are estimable within each microplate in spite of the existence of row and column effects. The (M, S)-criterion is used to select optimal and eliminate inefficient designs. It turns out that all (M, S)-optimal designs are binary, that is, no treatments appear twice in any row or column. Optimal designs are not unique with respect to design isomorphism. A series of (M, S)-optimal designs is constructed and all paired comparisons of treatments in the constructed designs are estimable regardless of the two-way heterogeneity. An (M, S)-optimal design for 8 ×12 microplates is provided and optimal designs of other dimensions can be constructed systematically.

[1]  C. S. Lin,et al.  A Modified Augmented Design for an Early Stage of Plant Selection Involving a Large Number of Test Lines without Replication , 1983 .

[2]  Robert Nadon,et al.  Statistical practice in high-throughput screening data analysis , 2006, Nature Biotechnology.

[3]  E. Sonnemann,et al.  U-Optimum row-columns designs for the comparison of two treatments , 1985 .

[4]  Xiaohua Douglas Zhang,et al.  Novel Analytic Criteria and Effective Plate Designs for Quality Control in Genome-Scale RNAi Screens , 2008, Journal of biomolecular screening.

[5]  Mike Jacroux.  Some E-optimal row−column designs having unequally replicated treatments , 1990 .

[6]  Hira Lal Agrawal.  Some Systematic Methods of Construction of Designs for TwoWay Elimination of Heterogeneity* , 1966 .

[7]  Bert Gunter,et al.  Improved Statistical Methods for Hit Selection in High-Throughput Screening , 2003, Journal of biomolecular screening.

[8]  B. K. Lundholt,et al.  A Simple Technique for Reducing Edge Effect in Cell-Based Assays , 2003, Journal of biomolecular screening.

[9]  D. Raghavarao,et al.  Constructions and Combinatorial Problems in Design of Experiments , 1972 .

[10]  Hiralal Agrawal.  Some Methods of Construction of Designs for Two-Way Elimination of Heterogeneity—1 , 1966 .

[11]  Ching-Shui Cheng,et al.  A note on (m.s)-optimality , 1978 .

[12]  Ching-Shui Cheng,et al.  Optimality and Construction of Pseudo-Youden Designs , 1981 .

[13]  Valentin Parvu,et al.  Optimal Row-Column Design for Three Treatments , 2007 .

[14]  S. S. Shrikhande,et al.  Designs for two-way elimination of heterogeneity , 1951 .

[15]  Theophilus Ogunyemi,et al.  On the connectedness of saturated square designs , 2009 .

[16]  K. H. Chew,et al.  A sufficient condition for nonvanishing of determinants , 1974 .

[17]  N. Gaffke,et al.  SOME CLASSES OF OPTIMALITY CRITERIA AND OPTIMAL DESIGNS FOR COMPLETE TWO-WAY LAYOUTS , 1981 .

[18]  J. Kunert.  On the use of the factor-sparsity assumption to get an estimate of the variance in saturated designs , 1997 .

[19]  Ching-Shui Cheng,et al.  Some Optimal Row-Column Designs , 2011 .

[20]  J. Kiefer.  Construction and optimality of generalized Youden designs II , 1975 .

[21]  Aloke Dey,et al.  A class of saturated row-column designs , 2010 .

[22]  J. John,et al.  Cyclic and Computer Generated Designs , 1995 .

[23]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[24]  M Kathleen Kerr,et al.  Design considerations for efficient and effective microarray studies. , 2003, Biometrics.

[25]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[26]  H. Wolkowicz,et al.  Bounds for eigenvalues using traces , 1980 .