Efficient two-sample designs for microarray experiments with biological replications
Jobst Landgrebe1, Frank Bretz2 and Edgar Brunner3,*
1 Abteilung Biochemie II, Universität Göttingen, Heinrich-Düker-Weg 12, D-37073 Göttingen
In the last years, biostatistical research has begun to apply linear models and design theory to develop efficient experimental designs and analysis tools for gene expression microarray data. With two-colour microarrays, direct comparisons of RNA-targets are possible and lead to incomplete block designs. In this setting, efficient designs for simple and factorial microarray experiments have mainly been proposed for technical replicates. But for biological replicates, which are crucial to obtain inference that can be generalised to a biological population, this question has only been discussed recently and is not fully solved yet. In this paper, we propose efficient designs for independent two-sample experiments using two-colour microarrays enabling biologists to measure their biological random samples in an efficient manner to draw generalisable conclusions. We give advice for experimental situations with differing group sizes and show the impact of different designs on the variance and degrees of freedom of the test statistics. The designs proposed in this paper can be evaluated using SAS PROC MIXED or S+/R lme.
Key words: microarray, design, biological replication, mixed linear model, ANOVA