Generalization of the normal-exponential model: exploration of a more accurate parametrisation for the signal distribution on Illumina BeadArrays

BACKGROUND: Illumina BeadArray technology includes non specific negative control features that allow a precise estimation of the background noise. As an alternative to the background subtraction proposed in BeadStudio which leads to an important loss of information by generating negative values, a background correction method modeling the observed intensities as the sum of the exponentially distributed signal and normally distributed noise has been developed. Nevertheless, Wang and Ye (2012) display a kernel-based estimator of the signal distribution on Illumina BeadArrays and suggest that a gamma distribution would represent a better modeling of the signal density. Hence, the normal-exponential modeling may not be appropriate for Illumina data and background corrections derived from this model may lead to wrong estimation. RESULTS: We propose a more flexible modeling based on a gamma distributed signal and a normal distributed background noise and develop the associated background correction, implemented in the R-package NormalGamma. Our model proves to be markedly more accurate to model Illumina BeadArrays: on the one hand, it is shown on two types of Illumina BeadChips that this model offers a more correct fit of the observed intensities. On the other hand, the comparison of the operating characteristics of several background correction procedures on spike-in and on normal-gamma simulated data shows high similarities, reinforcing the validation of the normal-gamma modeling. The performance of the background corrections based on the normal-gamma and normal-exponential models are compared on two dilution data sets, through testing procedures which represent various experimental designs. Surprisingly, we observe that the implementation of a more accurate parametrisation in the model-based background correction does not increase the sensitivity. These results may be explained by the operating characteristics of the estimators: the normal-gamma background correction offers an improvement in terms of bias, but at the cost of a loss in precision. CONCLUSIONS: This paper addresses the lack of fit of the usual normal-exponential model by proposing a more flexible parametrisation of the signal distribution as well as the associated background correction. This new model proves to be considerably more accurate for Illumina microarrays, but the improvement in terms of modeling does not lead to a higher sensitivity in differential analysis. Nevertheless, this realistic modeling makes way for future investigations, in particular to examine the characteristics of pre-processing strategies.