Journal of Computational Biology

A major goal of microarray experiments is to determine which genes are differentially expressed between samples. Differential expression has been assessed by taking ratios of expression levels of different samples at a spot on the array and flagging spots (genes) where the magnitude of the fold difference exceeds some threshold. More recent work has attempted to incorporate the fact that the variability of these ratios is not constant. Most methods are variants of Student's t-test. These variants standardize the ratios by dividing by an estimate of the standard deviation of that ratio; spots with large standardized values are flagged. Estimating these standard deviations requires replication of the measurements, either within a slide or between slides, or the use of a model describing what the standard deviation should be. Starting from considerations of the kinetics driving microarray hybridization, we derive models for the intensity of a replicated spot, when replication is performed within and between arrays. Replication within slides leads to a beta-binomial model, and replication between slides leads to a gamma-Poisson model. These models predict how the variance of a log ratio changes with the total intensity of the signal at the spot, independent of the identity of the gene. Ratios for genes with a small amount of total signal are highly variable, whereas ratios for genes with a large amount of total signal are fairly stable. Log ratios are scaled by the standard deviations given by these functions, giving model-based versions of Studentization. An example is given.