Distribution modeling and simulation of gene expression data

Data derived from gene expression microarrays often are used for purposes of classification and discovery. Many methods have been proposed for accomplishing these and related aims, however the statistical properties of such methods generally are not well established. To this end, it is desirable to develop realistic mathematical and statistical models that can be used in a simulation context so that the impacts of data analysis methods and testing approaches can be established. A method is developed in which variation among arrays can be characterized simultaneously for a large number of genes resulting in a multivariate model of gene expression. The method is based on selecting mathematical transformations of the underlying expression measures such that the transformed variables follow approximately a Gaussian distribution, and then estimating associated parameters, including correlations. The result is a multivariate normal distribution that serves to model transformed gene expression values within a subject population, while accounting for covariances among genes and/or probes. This model then is used to simulate microarray expression and probe intensity data by employing a modified Cholesky matrix factorization technique which addresses the singularity problem for the “small nn, big pp” situation. An example is given using prostate cancer data and, as an illustration, it is shown how data normalization can be investigated using this approach.