Generalized beta convolution model of the true intensity for the Illumina BeadArrays

Abstract

Microarray data come from many steps of production and have been known to contain noise. The pre-processing is implemented to reduce the noise, where the background is corrected. Prior to further analysis, many Illumina BeadArrays users had applied the convolution model, a model which had been adapted from when it was first developed on the Affymetrix platform, to adjust the intensity value: corrected background intensity value. Several models based on different underlying distributions and or parameters estimation methods have been proposed and applied. For instance : the exponential-gamma, the normal-gamma and the exponential-normal convolutions with a maximum likelihood estimation, non-parametric, Bayesian and moment methods of the parameters estimation, including two recent exponential-lognormal and gamma-lognormal convolutions. In this paper, we propose models and derive the corrected background intensity based on the generalized betas and the generalized beta-normal convolutions as a generalization of the existing models.