A study of convolution models for background correction of BeadArrays

Abstract

The RMA, since its introduction in \cite{Iri03a, Iri03b, Iri06}, 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 Affymetrix to the Illumina platform. The Illumina design has provided 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 the convolution model to compute the true intensity estimator. The availability of benchmarking data set at Illumina platform, the {\it Illumina spike-in}, helps researchers to evaluate their proposed method for Illumina BeadArrays. 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, where the intensity value is exponentially or gamma distributed and the noise has lognormal distribution. We compare the performance of the models on the Illumina spike-in data set, based on various criteria, for example, root and mean square error, $L_{1}$ error, Kullback-Leibler coefficient, and some adapted criteria from Affycomp \cite{Cop04}. We then provide a simulation study to measure the consistency of the error of background correction and the parametrization. We also study the performance of all models on the FFPE data set. Our study shows that our GLNn model is the optimal one for the benchmarking data set with benchmarking criteria, while the gamma-normal model has the best performance for the benchmarking data set with simulation criteria. At the public data set of FFPE, the gamma-normal and the exponential-gamma models with MLE cannot be used and our proposed models ELN and GLN have the best performance, showing a moderate error in background correction and in the parametrization.