Poisson regression models for interval censored count data.

In this dissertation, we develop Bayesian models for interval censored Poisson counts in the presence of zero inflation and missing data. As a motivating example, we consider data arising from a Human Immunodeficiency Virus (HIV) vaccine trial featuring imprecise counts, missing data, and an abundance of values which are either exactly observed to be zero or are left censored. We compare frequentist and Bayesian generalized linear mixed models of the lower limits of the intervals when the data contain no missing values. We then propose a likelihood which models the lower and upper limits of the observed intervals and accomodates zero inflation. Next, we present a simulation study comparing models of the intervals or lower limits to the precise count models. Finally, we apply the model of interval-censored Poisson counts to the HIV data and discuss the conclusions that are drawn from each analysis.