title: A statistical model for the analysis of beta values in DNA methylation studies.
abstract: 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. Using simulated data and a real sample of DNA methylation data from the Heinz Nixdorf Recall cohort study, we demonstrate that the proposed model fits our data significantly better than beta regression and M-value regression.
  
  
  CONCLUSIONS
  The proposed model contributes to an improved 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.
authors.affiliation: Department of Medical Biometry, Informatics and Epidemiology, University of Bonn, Sigmund-Freud-Str. 25, Bonn, D-53127, Germany. weinhold@imbie.uni-bonn.de.
authors.forename: Leonie
authors.initials: L
authors.lastname: Weinhold
authors.affiliation: Research Unit of Molecular Epidemiology, Helmholtz Zentrum München, Ingolstädter Landstr. 1, Neuherber, D-85764, Germany.
authors.forename: Simone
authors.initials: S
authors.lastname: Wahl
authors.affiliation: Department of Medical Informatics, Biometry and Epidemiology, University Hospital Essen, Hufelandstr. 55, Essen, D-45122, Germany.
authors.forename: Sonali
authors.initials: S
authors.lastname: Pechlivanis
authors.affiliation: Human Genomics Research Group, Department of Biomedicine, University Hospital Basel, Hebelstr. 20, Basel, CH-4031, Switzerland.
authors.forename: Per
authors.initials: P
authors.lastname: Hoffmann
authors.affiliation: Department of Medical Biometry, Informatics and Epidemiology, University of Bonn, Sigmund-Freud-Str. 25, Bonn, D-53127, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Schmid
mesh_terms: D000368:Aged; D000375:Aging / Q000235:genetics; D001519:Behavior; D015331:Cohort Studies; D003198:Computer Simulation; D018899:CpG Islands / Q000235:genetics; D019175:DNA Methylation / Q000235:genetics*; D006801:Humans; D008875:Middle Aged; D015233:Models, Statistical; D012907:Smoking / Q000235:genetics
keywords: Bounded response variables; DNA methylation; Gamma Regression; Gradient Boosting; HumanMethylation450k BeadChip