Bayesian estimation of fold-changes in the analysis of gene expression: The PFOLD algorithm

A general and detailed noise model for the DNA microarray measurement of gene expression is presented and used to derive a Bayesian estimation scheme for expression ratios, implemented in a program called PFOLD, which provides not only an estimate of the fold-change in gene expression, but also confidence limits for the change and a P-value quantifying the significance of the change. Although the focus is on oligonucleotide microarray technologies, the scheme can also be applied to cDNA based technologies if parameters for the noise model are provided. The model unifies estimation for all signals in that it provides a seamless transition from very low to very high signal-to-noise ratios, an essential feature for current microarray technologies for which the median signal-to-noise ratios are always moderate. The dual use, as decision statistics in a two-dimensional space, of the P-value and the fold-change is shown to be effective in the ubiquitous problem of detecting changing genes against a background of unchanging genes, leading to markedly higher sensitivities, at equal selectivity, than detection and selection based on the fold-change alone, a current practice until now.