Statistical analysis and significance testing of serial analysis of gene expression data using a Poisson mixture model

BACKGROUND: Serial analysis of gene expression (SAGE) is used to obtain quantitative snapshots of the transcriptome. These profiles are count-based and are assumed to follow a Binomial or Poisson distribution. However, tag counts observed across multiple libraries (for example, one or more groups of biological replicates) have additional variance that cannot be accommodated by this assumption alone. Several models have been proposed to account for this effect, all of which utilize a continuous prior distribution to explain the excess variance. Here, a Poisson mixture model, which assumes excess variability arises from sampling a mixture of distinct components, is proposed and the merits of this model are discussed and evaluated. RESULTS: The goodness of fit of the Poisson mixture model on 15 sets of biological SAGE replicates is compared to the previously proposed hierarchical gamma-Poisson (negative binomial) model, and a substantial improvement is seen. In further support of the mixture model, there is observed: 1) an increase in the number of mixture components needed to fit the expression of tags representing more than one transcript; and 2) a tendency for components to cluster libraries into the same groups. A confidence score is presented that can identify tags that are differentially expressed between groups of SAGE libraries. Several examples where this test outperforms those previously proposed are highlighted. CONCLUSION: The Poisson mixture model performs well as a) a method to represent SAGE data from biological replicates, and b) a basis to assign significance when testing for differential expression between multiple groups of replicates. Code for the R statistical software package is included to assist investigators in applying this model to their own data.