A Study of Convolution Models for Background Correction of BeadArrays

Abstract

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 popularityamong bioinformaticians. It has evolved from the exponential-normal convolution to thegamma-normal convolution, from single to two channels and from the Aymetrix to theIllumina 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 canapply a convolution model to compute the true intensity estimator.In this paper, we study the existing convolution models for background correction ofIllumina 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 haslognormal distribution.Our study shows that one of our proposed models, the gamma-lognormal with themethod 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 bestperformance for the benchmarking data set with simulation criteria.For the publicly available data sets, the gamma-normal and the exponential-gammamodels with maximum likelihood estimation method can not be used and our proposedmodels exponential-lognormal and gamma-lognormal have the best performance, showinga moderate error in background correction and in the parametrization.