Designs with Blocks of Size Two and Applications to Microarray Experiments

摘要

Designs with blocks of size two have numerous applications. Inudexperimental situations where observation loss is common, it is im-udportant for a design to be robust against breakdown. For designsudwith one treatment factor and a single blocking factor, with blocksudof size two, conditions for connectivity and robustness are obtainedudusing combinatorial arguments and results from graph theory. Lowerudbounds are given for the breakdown number in terms of design pa-udrameters. For designs with equal or near equal treatment replication,udthe concepts of treatment and block partitions, and of linking blocks,udare used to obtain information on the number of blocks required toudguarantee various levels of robustness. The results provide guidanceudfor construction of designs with good robustness properties.udRobustness conditions are also established for row column designsudin which one of the blocking factors involves blocks of size two. Suchuddesigns are particularly relevant for microarray experiments, whereudthe high risk of observation loss makes robustness important. Dis-udconnectivity in row column designs can be classified as three types.udTechniques are given to assess design robustness according to eachudtype, leading to lower bounds for the breakdown number. Guidanceudis given for robust design construction.udCyclic designs and interwoven loop designs are shown to have goodudrobustness properties.