Uncovering Alterations in Cancer Epigenetics via Trans-Dimensional Markov Chain Monte Carlo and Hidden Markov Models.

Epigenetic alterations are key drivers in the development and progression of cancer. Identifying differentially methylated cytosines (DMCs) in cancer samples is a crucial step toward understanding these changes. In this paper, we propose a trans-dimensional Markov chain Monte Carlo (TMCMC) approach that uses hidden Markov models (HMMs) with binomial emission, and bisulfite sequencing (BS-Seq) data, called DMCTHM , to identify DMCs in cancer epigenetic studies. We introduce the Expander-Collider penalty to tackle under and overestimation in TMCMC-HMMs. We address all known challenges inherent in BS-Seq data by introducing novel approaches for capturing functional patterns and autocorrelation structure of the data, as well as for handling missing values, multiple covariates, multiple comparisons, and family-wise errors. We demonstrate the effectiveness of DMCTHM through comprehensive simulation studies. The results show that our proposed method outperforms other competing methods in identifying DMCs. Notably, with DMCTHM , we uncovered new DMCs and genes in Colorectal cancer that were significantly enriched in the Tp53 pathway.