Modelling RNA‐Seq data with a zero‐inflated mixture Poisson linear model

Abstract

RNA sequencing (RNA‐Seq) has been frequently used in genomic studies and has generated a vast amount of data. The RNA‐Seq data are composed of two parts: (a) a sequence of nucleotides of the genome; and (b) a corresponding sequence of counts, standing for the number of short reads whose mapped positions start at each position of the genome. One common feature of these count data is that they are typically nonuniform; recent studies have revealed that the nonuniformity is partially owing to a systematic bias resulted from the sequencing preference. Existing works in the literature model the nonuniformity with a single component Poisson linear model that incorporates the effects of the sequencing preference. However, we observe consistently that the short reads mapped to a gene may have a mixture structure and can be zero‐inflated. A single component model may not suffice to model the complexity of such data. In this paper, we propose a zero‐inflated mixture Poisson linear model for the RNA‐Seq count data and derive a fast expectation–maximisation‐based algorithm for estimating the unknown parameters. Numerical studies are conducted to illustrate the effectiveness of our method.

Fisher-Pitman permutation tests based on nonparametric Poisson mixtures with application to single cell genomics

“…This section applies the studied permutation tests to a scRNA-seq data. There has been a large literature studying fitting RNA-seq data using Poisson mixtures including, e.g., over-dispersed Poisson model (Robinson et al, 2010), Poisson-Gamma model (Love et al, 2014;Huang et al, 2018), Poisson-Beta model (Vu et al, 2016), Poisson-log normal model (Silva et al, 2019), Poisson mixture model with K-clusters (Rau et al, 2015), finite Poisson mixture models (Wu et al, 2013), zeroinflated mixture Poisson linear models (Liu et al, 2019), Poisson mixture models with unimodal mixing distributions (Lu, 2018). Compared to parametric Poisson mixture models, nonparametric Poisson mixture models haven't received much attention; some notable exceptions include Bi and Davuluri (2013), Dadaneh et al (2018), Sarkar and Stephens (2021), the latter of which was closely followed by us.…”