Zero-Inflated Negative Binomial (ZINB) regression model for over-dispersed count data with excess zeros and repeated measures, an application to human microbiota sequence data

In many biomedical applications, count outcomes are fairly common and often these count data have a large number of zeros. Zero-inflated regression models are useful for analyzing such data. Moreover, the non-zero observations may be over-dispersed in relation to the Poisson distribution, biasing parameter estimates and underestimating standard errors. In such a circumstance, a Zero-Inflated Negative Binomial (ZINB) regression model better accounts for these characteristics compared to a Zero-Inflated Poisson (ZIP). In addition, repeated measures are often collected on the same individual subjects, random effects are introduced to account for the within subject variation. The objective of this thesis is to present a ZINB regression model for over-dispersed count data with excess zeros and repeated measures. This mixture model contains components to model the probability of excess zero values and the negative binomial parameters, allowing for repeated measures using independent random effects between these two components. Parameter estimation is achieved by maximizing an appropriate likelihood function using a stable numerical procedure such as the Newton-Raphson algorithm. A small simulation study was performed for model verification and application of the proposed model is applied to data from a human microbiota study.