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

Abstract

SummaryThe zero-inflated negative binomial (ZINB) distribution has been widely used for count data analyses in various biomedical settings due to its capacity of modeling excess zeros and overdispersion. When there are correlated count variables, a bivariate model is essential for understanding their full distributional features. For this purpose, we develop a Bivariate Zero-Inflated Negative Binomial (BZINB) model that has a simple latent variable framework and parameters with intuitive interpretations. Using this model, we examine two biomedical data examples where the counts are zero-inflated—single cell RNA sequencing (scRNA-seq) data and dental caries count indices. In scRNA-seq data example, a correlation between a pair of genes is estimated after adjusting for the effects of dropout events represented by excess zeros. In the dental caries data, we analyze how the treatment with Xylitol mints affects the marginal mean and other patterns of response manifested in the two dental caries traits. An R package ‘bzinb’ is available on CRAN.