Flexible pooling in gene expression profiles: design and statistical modeling of experiments for unbiased contrasts

Pooling is an important resource in microarray gene expression experiments. Due to restrictions imposed by the statistical analysis it is widespread practice to employ a fixed pool size over the whole experiment. But this limits the efficient use of experimental material. In this paper we propose a design with flexible pool sizes for mRNA pooling which includes varying numbers of experimental units per pool. Enforcing balance between the pool sizes of every treatment level, we show the unbiasedness of the generalized least squares estimator of a contrast testing for differences in gene expression between treatments. In order to model the variability of pooled observations we include random biological effects as well as a special kind of technical error (random effect for mixtures), induced by inaccuracies in blending aliquots of mRNA from different individuals into common pools. Results for one-color arrays are also extended to two-color arrays.