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The robust multi-array average (RMA), since its introduction in Irizarry, Bolstad, Collin, Cope, Hobbs, and Speed (2003a); Irizarry, Hobbs, Collin, Beazer-Barclay, An- tonellis, Scherf, and Speed (2003b); Irizarry, Wu, and Jaee (2006), has gained popularity among bioinformaticians. It has evolved from the exponential-normal convolution to the gamma-normal convolution, from single to two channels and from the Aymetrix to the Illumina platform. The Illumina design provides two probe types: the regular and the control probes. This design is very suitable for studying the probability distribution of both and one can apply a convolution model to compute the true intensity estimator. In this paper, we study the existing convolution models for background correction of Illumina BeadArrays in the literature and give a new estimator for the true intensity, assuming that the intensity value is exponentially or gamma distributed and the noise has lognormal distribution. Our study shows that one of our proposed models, the gamma-lognormal with the method of moments for parameters estimation, is the optimal one for the benchmark- ing data set with benchmarking criteria, while the gamma-normal model has the best performance for the benchmarking data set with simulation criteria. For the publicly available data sets, the gamma-normal and the exponential-gamma models with maximum likelihood estimation method can not be used and our proposed models exponential-lognormal and gamma-lognormal have the best performance, showing a moderate error in background correction and in the parametrization.

A Study of Convolution Models for Background Correction of BeadArrays