Optimal Row–Column Designs in High-Throughput Screening Experiments

Abstract

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.