Interval-censored negative binomial models : a Bayesian approach.




Doherty, Stephanie Michelle.

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Count data are quite common in many research areas. Interval-censored counts, in which an interval representing a range of counts is observed rather than the precise count, may arise in many situations, including survey data. In this dissertation we develop a model for accommodating interval-censored count data through the interval-censored negative binomial model, with an expansion to a regression model in which the interval count responses are regressed on covariate values. We employ both frequentist and Bayesian methods to arrive at point and interval estimates for the negative binomial parameters. We nd that many factors, including the interval-censored widths and the tendency of the precise counts toward either endpoint of the intervals, a ect parameter estimates based on interval-censored data as compared to estimates using only precise data. We perform simulation studies in the non-regression and regression contexts, which compare the interval-censored model to alternatives for accommodating interval-censored data. These methods are precise-count analyses based on the lower endpoints, upper endpoints, or means of the observed intervals. For the scenarios in our simulation experiments, we nd that the interval-censored model outperforms the lower endpoint and upper endpoint methods, and performs at least as well as, or better than, the mean method. We conclude with an extended example, in which we compare the interval-censored method to the lower and upper endpoint methods for health-related quality of life survey data that are interval-censored. We nd that the interval-censored method allows us to calculate parameter estimates and conduct posterior inferences, without the need to discard any information provided in the study.