Basic Properties and Information Theory of Audic-Claverie Statistic for Analyzing cDNA Arrays

Background: The Audic-Claverie method [1] has been and still continues to be a popular approach for detection of differentially expressed genes in the SAGE framework. The method is based on the assumption that under the null hypothesis tag counts of the same gene in two libraries come from the same but unknown Poisson distribution. The problem is that each SAGE library represents only a single measurement. We ask: Given that the tag count samples from SAGE libraries are extremely limited, how useful actually is the Audic-Claverie methodology? We rigorously analyze the A-C statistic that forms a backbone of the methodology and represents our knowledge of the underlying tag generating process based on one observation. Results: We show that the A-C statistic and the underlying Poisson distribution of the tag counts share the same mode structure. Moreover, the K-L divergence from the true unknown Poisson distribution to the A-C statistic is minimized when the A-C statistic is conditioned on the mode of the Poisson distribution. Most importantly, the expectation of this K-L divergence never exceeds 1/2 bit. Conclusion: A rigorous underpinning of the Audic-Claverie methodology has been missing. Our results constitute a rigorous argument supporting the use of Audic-Claverie method even though the SAGE libraries represent very sparse samples.