A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Abstract

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference, Journal of Theoretical Biology, doi:10.1016Biology, doi:10. /j.jtbi.2010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Fundamental probability models and statistical inference 302-831-1048)A c c e p t e d m a n u s c r i p t 2 AbstractGene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.

Evaluation of Bias-Variance Trade-Off for Commonly Used Post-Summarizing Normalization Procedures in Large-Scale Gene Expression Studies

“…In addition, we conduct several simulation studies based on a widely adopted random effect model used in [15], [36]–[38]:In this model, represents variation that is the same for every gene and specific to the th array. While it is known that log transformation stabilizes variance for microarray data, more advanced variance stabilization transformation techniques [39], [40] can achieve better uniformity of gene-specific variation.…”

Decreased Secretion and Unfolded Protein Response Upregulation

“…A new mixture model method in which transformed signal intensities are characterized by a set of overlapping beta distributions is also a good choice for selecting differentially expressed genes in a two-state experiment (Ogunnaike et al ., 2010). Starting from first principles, the authors showed that this distribution is an adequate descriptor of microarray data and from the set of overlapping fits they calculate the probability that a gene is upregulated, downregulated, or not regulated (Ogunnaike et al ., 2010).…”

“…Starting from first principles, the authors showed that this distribution is an adequate descriptor of microarray data and from the set of overlapping fits they calculate the probability that a gene is upregulated, downregulated, or not regulated (Ogunnaike et al ., 2010). Replicates can be used to calculate a confidence metric for the reported probabilities (Ogunnaike et al ., 2010).…”

“…Starting from first principles, the authors showed that this distribution is an adequate descriptor of microarray data and from the set of overlapping fits they calculate the probability that a gene is upregulated, downregulated, or not regulated (Ogunnaike et al ., 2010). Replicates can be used to calculate a confidence metric for the reported probabilities (Ogunnaike et al ., 2010). This method has the advantages of requiring no replicates and of leveraging all the data in making decisions about the differential expression of each gene, an approach that recognizes gene expression values are not independent (Ogunnaike et al ., 2010).…”

“…Replicates can be used to calculate a confidence metric for the reported probabilities (Ogunnaike et al ., 2010). This method has the advantages of requiring no replicates and of leveraging all the data in making decisions about the differential expression of each gene, an approach that recognizes gene expression values are not independent (Ogunnaike et al ., 2010). Furthermore, it slightly outperformed SAM in a simulation study, recovering 99.6% of differentially expressed genes with five replicates, although SAM’s performance is still remarkable with a recovery of 94.7% of the genes (Ogunnaike et al ., 2010).…”