Assessing statistical precision, power, and robustness of alternative experimental designs for two color microarray platforms based on mixed effects models

Recommendations on experimental designs for two color microarray systems have been generally conflicting as they pertain to the general choice between reference and non-reference loop designs. This conflict may currently exist because many previously published assessments may not have effectively connected design layout with the level of biological relative to technical replication. We reassess various reference and non-reference designs for statistical efficiency in terms of standard errors of mean differences, power of test, and robustness using recently developed mixed model software tools. In minimally replicated cases (n = 2), it appears that the reference design outperforms the classical loop design whereby a sample from each animal is used for only one particular array hybridization. Alternatively, the reference design was consistently inferior to those connected loop designs in which a sample from each animal is used in two different hybridizations. Nevertheless, the gap in power between these two designs diminished as the biological to residual variance ratio increased. The statistical efficiency of a single large classical loop design for the comparison of many treatments was demonstrated to be highly sensitive to missing arrays relative to a common reference design (n = 2). However, the use of two loops within an interwoven loop design was shown to be substantially more robust to missing arrays and statistically more efficient relative to a common reference design. Furthermore, the use of more than one loop leads to less disparity in precision and power comparisons between any two treatments.