Efficient statistical methods for detecting differential methylation

Addition of the methyl group to the 5-position of a cytosine (5mC) is the most commonly studied epigenetic modification on DNA, and its effects on different diseases and cancer have been widely studied. We have previously developed a hierarchical generative model, LuxGLM, for analysing 5mC and oxidized methylcytosine species (oxi-mC). LuxGLM combines a generative model for sequencing data with a general linear model component to account for confounding effects, and the tool is shown to provide accurate detection of differential methylation when compared to other state-of-the-art methods. However, detecting differential cytosine methylation for a whole genome is a computationally cumbersome task. In LuxGLM, Bayes factors are calculated for the hypothesis testing to detect differential methylation. Originally, the Savage-Dickey estimate of the Bayes factor was used and the approximation is done by utilizing standard Hamiltonian Monte Carlo sampling feature of probabilistic programming language Stan. To increase the computational efficiency, we propose using variational inference feature of Stan for the calculation of the Bayes factor. Variational inference can be used for efficient posterior sampling and combine that with the Savage-Dickey estimate, or we can use the expectation lower bound directly as an approximation of Bayes factor. By adjusting the parameters of the variational inference, we can get equally good results with lower computation times. This makes LuxGLM an attractive method even for whole-genome analysis.