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 over-estimation 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.