title: Validation and characterization of DNA microarray gene expression data distribution and associated moments.
abstract: BACKGROUND
  The data from DNA microarrays are increasingly being used in order to understand effects of different conditions, exposures or diseases on the modulation of the expression of various genes in a biological system. This knowledge is then further used in order to generate molecular mechanistic hypotheses for an organism when it is exposed to different conditions. Several different methods have been proposed to analyze these data under different distributional assumptions on gene expression. However, the empirical validation of these assumptions is lacking.
  
  
  RESULTS
  Best fit hypotheses tests, moment-ratio diagrams and relationships between the different moments of the distribution of the gene expression was used to characterize the observed distributions. The data are obtained from the publicly available gene expression database, Gene Expression Omnibus (GEO) to characterize the empirical distributions of gene expressions obtained under varying experimental situations each of which providing relatively large number of samples for hypothesis testing. All data were obtained from either of two microarray platforms--the commercial Affymetrix mouse 430.2 platform and a non-commercial Rosetta/Merck one. The data from each platform were preprocessed in the same manner.
  
  
  CONCLUSIONS
  The null hypotheses for goodness of fit for all considered univariate theoretical probability distributions (including the Normal distribution) are rejected for more than 50% of probe sets on the Affymetrix microarray platform at a 95% confidence level, suggesting that under the tested conditions a priori assumption of any of these distributions across all probe sets is not valid. The pattern of null hypotheses rejection was different for the data from Rosetta/Merck platform with only around 20% of the probe sets failing the logistic distribution goodness-of-fit test. We find that there are statistically significant (at 95% confidence level based on the F-test for the fitted linear model) relationships between the mean and the logarithm of the coefficient of variation of the distributions of the logarithm of gene expressions. An additional novel statistically significant quadratic relationship between the skewness and kurtosis is identified. Data from both microarray platforms fail to identify with any one of the chosen theoretical probability distributions from an analysis of the l-moment ratio diagram.
authors.affiliation: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA. mehrotra@iems.northwestern.edu
authors.forename: Reuben
authors.initials: R
authors.lastname: Thomas
authors.forename: Luis
authors.initials: L
authors.lastname: de la Torre
authors.forename: Xiaoqing
authors.initials: X
authors.lastname: Chang
authors.forename: Sanjay
authors.initials: S
authors.lastname: Mehrotra
mesh_terms: D030541:Databases, Genetic; D015870:Gene Expression; D020869:Gene Expression Profiling / Q000379:methods*; D016015:Logistic Models; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*