A bivariate zero-inflated negative binomial model and its applications to biomedical settings

Abstract

Measuring gene-gene dependence in single cell RNA sequencing (scRNA-seq) count data is often of interest and remains challenging, because an unidentified portion of the zero counts represent non-detected RNA due to technical reasons. Conventional statistical methods that fail to account for technical zeros incorrectly measure the dependence among genes. To address this problem, we propose a bivariate zero-inflated negative binomial (BZINB) model constructed using a bivariate Poisson-gamma mixture with dropout indicators for the technical (excess) zeros. Parameters are estimated based on the EM algorithm and are used to measure the underlying dependence by decomposing the two sources of zeros. Compared to existing models, the proposed BZINB model is specifically designed for estimating dependence and is more flexible, while preserving the marginal zero-inflated negative binomial distributions. Additionally, it has a simple latent variable framework, allowing parameters to have clear and intuitive interpretations, and its computation is feasible with large scale data. Using a recent scRNA-seq dataset, we illustrate model fitting and how the model-based measures can be different from naive measures. The inferential ability of the proposed model is evaluated in a simulation study. An R package 'bzinb' is available on CRAN.

BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data

“…Of course, there are cases where negative correlations are of interest; for example, in the context of species competition, other correlation measures could be used. If negative correlations are also of interest in network visualizations and strong −0.3) [ 41 ] negative Spearman correlations were observed, the negative Spearman correlations could be directly used in place of near-zero BZINB model-based correlations, or the weighted Pearson correlation could be used by weighting the observed abundance counts by the model-based dropout probability as suggested in Cho et al 2021 [ 10 ]. However, incorporating negative correlations can introduce another layer of complexity to network analysis applications for multi-omics and cluster identification.…”

“…Cho et al 2021 [ 10 ] began by introducing a bivariate negative binomial (BNB) model based on the Poisson–Gamma mixture model. First, let for .…”

“…For correlation between a pair of genes in scRNaseq data, a bivariate zero-inflated (BZINB) model was proposed by Cho et al 2021 [ 10 ] that has the ZINB marginals, more parameters to flexibly accommodate the complexity of the single-cell biology, and the estimated correlation conditional for the non-dropout events. With similar assumptions of dropouts observed as excess zeros and the overdispersion problem accentuated in microbiome data, here we extend the BZINB framework for microbial data modeling to compute a unique correlation measured between species or between species and metabolites.…”

“…Our proposed method, BZINB-based integration of microbiome and metabolome for pathway analysis (BZINB-iMMPath), uses the newly developed bivariate zero-inflated negative binomial (BZINB) model to directly model the joint distribution of a pair of count vectors, where one vector represents microbial species and the other vector represents metabolites, to estimate model-based correlations. The advantage of our method, which uses BZINB, is that we can rigorously handle the excess zeros in the distribution of microbiome counts [ 10 ].…”

scLink: Inferring Sparse Gene Co-expression Networks from Single-cell Expression Data

“…However, these two measures cannot provide a robust estimation of gene co-expression given the sparse scRNA-seq data with substantial technical noises and biological heterogeneity [20,21].…”