Zipf's law in importance of genes for cancer classification using microarray data.

Area of Science:

• Bioinformatics
• Systems Biology
• Genomics

Background:

• Microarray analysis ranks genes based on differential expression between conditions.
• Gene expression data often exhibits complex statistical properties.
• Identifying truly significant genes requires robust analytical methods.

Purpose of the Study:

• To investigate the statistical distribution of ranked gene expression measures.
• To determine if gene expression ranking follows known power-law distributions.
• To understand the implications of these distributions for gene selection in microarray studies.

Main Methods:

• Utilized normalized maximum likelihood as a measure of differential gene expression.
• Applied logistic regression models to microarray datasets.
• Analyzed the rank-abundance relationship of gene expression measures.
• Examined permuted datasets to assess the robustness of observed patterns.

Main Results:

• The falling-off of differential gene expression measures as a function of rank follows a power-law distribution (Zipf's law).
• This power-law behavior was observed in both real and permuted datasets.
• The chi-squared distribution of likelihood ratios explains the presence of these power-law functions.
• An intrinsic cutoff between important and irrelevant genes is precluded by this power-law characteristic.

Conclusions:

• The universal presence of Zipf's law in ranked gene expression data has significant implications for gene selection strategies.
• Standard methods for identifying significant genes may need re-evaluation due to the absence of a clear intrinsic cutoff.
• Further characterization of ranked likelihood plots, including the rate of fall-off, is crucial for accurate microarray data interpretation.