A bivariate zero-inflated negative binomial model for identifying underlying dependence with application to single cell RNA sequencing data

Summary

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.