A Hierarchical Semi-Markov Model for Detecting Enrichment with Application to ChIP-Seq Experiments

Chromatin immunoprecipitation followed by direct sequencing (ChIP-Seq) has revolutionalized the experiments in profiling DNA-protein interactions and chromatin remodeling patterns. However, limited statistical tools are available for modeling and analyzing the ChIP-Seq data thoroughly. We carefully study the data generating mechanism of ChIP-Seq data and propose a new model-based approach for detecting enriched regions. Our model is based on a hierarchical mixture model which gives rise to a zero-inflated negative binomial (ZINB), coupled with a hidden semi-Markov model (HSMM) to address the sequencing depth and biases, the inherent spatial data structure and allows for detection of multiple non-overlapping variable size peaks. In particular, we demonstrate that the proposed ZINB accounts for the excess zeroes and over-dispersion in the observed data relative to a Poisson distribution, and this model provides a better fit as the background distribution. We also propose a new meta false discovery rate (FDR) control at peak level as an alternative to the usual heuristic postprocessing of enriched bins identified via bin level FDR control. We show with simulations and case studies that this new procedure allows for the boundaries of peak regions to be declared probabilistically and provides accurate FDR control.