DNA methylation profiles has become an alternative molecular footprint for classification. It occurs in the context of a CpG dinucleotide. It is an important epigenetic modification, which can be inherited through cell division. In this chemical modification of the cytosine nucleotide, the 5-carbon position is enzymatically modified by the addition of a methyl group such that cytosines can occur in a methylated or unmethylated state. CpG islands are usually not methylated in normal tissues but frequently become hypermethylated in cancer [1
]. This hypermethylation is associated with gene silencing [2
] and plays an important role in the inactivation of tumor suppressor genes. Most CpGs or CpG regions have been found to have a bimodal distribution of methylation profiles, either hypomethylated or hypermethylated [3
]. Unique methylation patterns have been shown to exist in diseases including various types of cancer [4
]. DNA methylation analysis promises to become a powerful tool in cancer diagnosis, with possible applications to the choice of treatment and prognostication. The high throughput methylation profiling technology has been developed to survey methylation status of more than 1500 CpG sites for a large collection of cancer genes and been specifically targeting. Studying how the methylation profiles can be used to distinguish different subtypes of the tumor has been a focus in current cancer research. But most existing algorithms working on methylation data are from sequence level. The exact levels of methylation expression are not fully considered yet.
To this end, clustering analysis is often used to identify methylation subgroups that are distinct from one another in data [5
]. However, the DNA methylation data presents unique challenges. First, it is not appropriate to cluster DNA methylation expressions using traditional clustering methods. The traditional k-means clustering algorithms are based on Gaussian Mixture Model (GMM) assumptions. In GMM, the individual data points are assumed to follow multivariate Gaussian distribution and thus the distance between two points can be evaluated by Euclidean distance conveniently. However, since "beta" values from DNA methylation array represent the percentage of the methylated alleles and are between 0[1
], traditional GMM is no longer appropriate. Instead, a mixture of the beta distribution [7
] would be a more accurate model. Second, a model selection process is often needed in clustering to determine the number of clusters, making the clustering analysis more complicated. A predefined number of clusters (or model) is required in the mixture distribution based methods (such as k-means). Since different number of clusters will yield different clustering results, a model selection process is desirable to determine the best number of clusters. The model selection is very different problem, whose optimal solution is of exponential complexity. The popular suboptimal solutions have been proposed that include minimum description length (MDL) and Bayesian information criterion (BIC). Although computationally efficient, these methods would fail when clusters are not well separated. The recent proposed nonparametric Bayesian methods including Dirichlet process (DP) provide an avenue that can lead to a better solution.
In a response to the aforementioned limitations, we proposed here a nonparametric Dirichlet process beta mixture model (DPBMM) method for clustering DNA methylation expression profiles produced by Illumina Infinium Beadchip. DPBMM makes use of Dirichlet process mixture to place a prior [9
] on cluster assignment, thus enables automatic determination of the optimal number of clusters. To perform the analytical intractable learning, an algorithm based on Gibbs sampling and "no-gap" sampling is developed to effectively infer all the relevant variables. The proposed DPBMM method builds an infinite beta mixture model to describe DNA methylation data, which is different from the finite beta mixture model in [8
]. We present a simulation study comparing its properties to RPMM (Recursively partitioned mixture model) employing BIC (Bayesian information criterior) in [8
]. The results demonstrated the better performance of our proposed method. Finally, we applied the DPBMM to the methylation array obtained from 55 Glioblastoma Multiform (GBM) brain tissue samples.