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

Abstract

The zero-inflated negative binomial 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. Examples include measuring correlation of two genes in sparse single-cell RNA sequencing data and modeling dental caries count indices on two different tooth surface types. For these purposes, we develop a richly parametrized bivariate zero-inflated negative binomial model that has a simple latent variable framework and eight free parameters with intuitive interpretations. In the scRNA-seq data example, the correlation 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 lozenges affects the marginal mean and other patterns of response manifested in the two dental caries traits. An R package “bzinb” is available on Comprehensive R Archive Network.

Modeling Adverse Events Counts in the Bulgarian Pharmacovigilance Database

“…This means that ZANBI can fit more complex models with multiple explanatory variables, while ZAPIG may struggle with complex models due to convergence issues. This can be explained with the fact that ZAPIG is more difficult to calculate and the necessity for the algorithms to use the recurrence relation (13). This is supported by the observation that the ZAPIG algorithm is several times slower than the ZANBI one especially with the more complex models.…”

“…NBI(µ,σ) is quite flexible with many different parametrizations and has been used to model a variety of data with mild to moderate overdispersion from various fields of study: CD4 counts in HIV-infected women [8], microbiome counts in mouse gut [9], rainfall counts [10], postfire conifer regeneration counts to examine seedling distributions [11], data from single-cell RNA sequencing [12] and dental caries count indices [13], prediction of micronuclei frequency as a biomarker for genotoxic exposure and cancer risk [14], a clinical trial to evaluate the effectiveness of a prehabilitation program in preventing functional disease among physically frail, community-living older persons [15], investigating the social and demographic factors associated with public awareness of health warnings on the harmful effects of environmental tobacco smoke [16], assessing highway crash frequency by injury severity [17], improving planning and management of urban trail traffic [18], modeling overdispersion in ecological count data, e. g., bird migration [19], and other applications of NB in ecology and biodiversity reviewed in [20], male satellites counts in the popular horseshoe crab data [21], modeling the dependence of tropical storm counts in the North Atlantic basin on climate indices [22], estimation of the reproduction number R 0 for SARS 2003 coronavirus by the number of secondary cases [23], predicting length of stay from an electronic patient record for patients with knee replacement [24], or for elderly patients [25], serial clustering of extratropical cyclones [26], or of intense European storms [27], digital gene expression counts [28].…”

Perfluorooctanoic Acid Promotes Recruitment and Exocytosis of Rodlet Cells in the Renal Hematopoietic Tissue of Common Carp

“…The negative binomial probability distribution, with applications in diverse biological and biomedical scenarios, signifies non-uniform cellular clustering stemming from factors such as cellular attraction, chemotaxis, spatial constraints, variations in cell proliferation rates, irregular migration patterns, or uneven resource distribution within tissues, particularly in situations characterised by overdispersion where variability exceeds that anticipated by a Poisson process [63][64][65][66][67][68][69][70].…”