  Background: The analysis of DNA methylation is a key component in the
development of personalized treatment approaches. A common way to measure DNA
methylation is the calculation of beta values, which are bounded variables of
the form M = (M + U) that are generated by Illumina's 450k BeadChip array. The
statistical analysis of beta values is considered to be challenging, as
traditional methods for the analysis of bounded variables, such as M-value
regression and beta regression, are based on regularity assumptions that are
often too strong to adequately describe the distribution of beta values.
Results: We develop a statistical model for the analysis of beta values that is
derived from a bivariate gamma distribution for the signal intensities M and U.
By allowing for possible correlations between M and U, the proposed model
explicitly takes into account the data-generating process underlying the
calculation of beta values. Conclusion: The proposed model can be used to
improve the identification of associations between beta values and covariates
such as clinical variables and lifestyle factors in epigenome-wide association
studies. It is as easy to apply to a sample of beta values as beta regression
and M-value regression.
