title: Zipf's law in importance of genes for cancer classification using microarray data.
abstract: Using a measure of how differentially expressed a gene is in two biochemically/phenotypically different conditions, we can rank all genes in a microarray dataset. We have shown that the falling-off of this measure (normalized maximum likelihood in a classification model such as logistic regression) as a function of the rank is typically a power-law function. This power-law function in other similar ranked plots are known as the Zipf's law, observed in many natural and social phenomena. The presence of this power-law function prevents an intrinsic cutoff point between the "important" genes and "irrelevant" genes. We have shown that similar power-law functions are also present in permuted dataset, and provide an explanation from the well-known chi(2) distribution of likelihood ratios. We discuss the implication of this Zipf's law on gene selection in a microarray data analysis, as well as other characterizations of the ranked likelihood plots such as the rate of fall-off of the likelihood.
authors.affiliation: Center for Genomics and Human Genetics North Shore LIJ Research Institute, 350 Community Drive, Manhasset, NY 11030, USA. wli@nlij-genetics.org
authors.forename: Wentian
authors.initials: W
authors.lastname: Li
authors.forename: Yaning
authors.initials: Y
authors.lastname: Yang
mesh_terms: D003937:Diagnosis, Differential; D020022:Genetic Predisposition to Disease; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D009369:Neoplasms / Q000175:diagnosis* / Q000235:genetics*; D020411:Oligonucleotide Array Sequence Analysis