**Detection of Di**ff**erentially Methylated Regions Using Bayes Factor for Ordinal Group Responses**

**Fengjiao Dunbar 1, Hongyan Xu 2, Duchwan Ryu 3, Santu Ghosh 2, Huidong Shi <sup>4</sup> and Varghese George 2,\***

<sup>1</sup> Genomics Research Center, AbbVie, North Chicago, IL 60064, USA; fengjiao.dunbar@abbvie.com

<sup>2</sup> Department of Population Health Sciences, Augusta University, Augusta, GA 30912, USA; hxu@augusta.edu (H.X.); sghosh@augusta.edu (S.G.)


Received: 19 July 2019; Accepted: 15 September 2019; Published: 17 September 2019

**Abstract:** Researchers in genomics are increasingly interested in epigenetic factors such as DNA methylation, because they play an important role in regulating gene expression without changes in the DNA sequence. There have been significant advances in developing statistical methods to detect differentially methylated regions (DMRs) associated with binary disease status. Most of these methods are being developed for detecting differential methylation rates between cases and controls. We consider multiple severity levels of disease, and develop a Bayesian statistical method to detect the region with increasing (or decreasing) methylation rates as the disease severity increases. Patients are classified into more than two groups, based on the disease severity (e.g., stages of cancer), and DMRs are detected by using moving windows along the genome. Within each window, the Bayes factor is calculated to test the hypothesis of monotonic increase in methylation rates corresponding to severity of the disease versus no difference. A mixed-effect model is used to incorporate the correlation of methylation rates of nearby CpG sites in the region. Results from extensive simulation indicate that our proposed method is statistically valid and reasonably powerful. We demonstrate our approach on a bisulfite sequencing dataset from a chronic lymphocytic leukemia (CLL) study.

**Keywords:** Bayes factor; Bayesian mixed-effect model; CpG sites; DNA methylation; Ordinal responses
