  As hypermethylation of promoter cytosine-guanine dinucleotide (CpG) islands
has been shown to silence tumour suppressor genes, identifying differentially
methylated CpG sites between different samples can assist in understanding
disease. Differentially methylated CpG sites (DMCs) can be identified using
moderated t-tests or nonparametric tests, but this typically requires the use
of data transformations due to a lack of appropriate statistical methods able
to adequately account for the bounded nature of DNA methylation data.
  We propose a family of beta mixture models (BMMs) which use a model-based
approach to cluster CpG sites given their original beta-valued methylation
data, with no need for transformations. The BMMs allow (i) objective inference
of methylation state thresholds and (ii) identification of DMCs between
different sample types. The BMMs employ different parameter constraints
facilitating application to different study settings. Parameter estimation
proceeds via an expectation-maximisation algorithm, with a novel approximation
in the maximization step providing tractability and computational feasibility.
  Performance of BMMs is assessed through thorough simulation studies, and the
BMMs are used to analyse a prostate cancer dataset. The BMMs objectively infer
intuitive and biologically interpretable methylation state thresholds, and
identify DMCs that are related to genes implicated in carcinogenesis and
involved in cancer related pathways. An R package betaclust facilitates
widespread use of BMMs.
