  Microarray data consists of mRNA expression levels of thousands of genes
under certain conditions. A difference in the expression level of a gene at two
different conditions/phenotypes, such as cancerous versus non-cancerous, one
subtype of cancer versus another, before versus after a drug treatment, is
indicative of the relevance of that gene to the difference of the high-level
phenotype. Each gene can be ranked by its ability to distinguish the two
conditions. We study how the single-gene classification ability decreases with
its rank (a Zipf's plot). Power-law function in the Zipf's plot is observed for
the four microarray datasets obtained from various cancer studies. This
power-law behavior in the Zipf's plot is reminiscent of similar power-law
curves in other natural and social phenomena (Zipf's law). However, due to our
choice of the measure of importance in classification ability, i.e., the
maximized likelihood in a logistic regression, the exponent of the power-law
function is a function of the sample size, instead of a fixed value close to 1
for a typical example of Zipf's law. The presence of this power-law behavior is
important for deciding the number of genes to be used for a discriminant
microarray data analysis.
