## Date of Award

1-1-2011

## Document Type

Campus Access Dissertation

## Department

Epidemiology and Biostatistics

## Sub-Department

Biostatistics

## First Advisor

Cheryl Addy

## Second Advisor

Hardin, James

## Abstract

Censoring is an issue common to the analysis of survival data. Survival analysis evaluates time to the occurrence of an event for each individual as its outcome measure; those individuals for whom the event does not occur prior to the end of the study are said to have censored event times. Censoring may also affect count data. Outcomes may only be known as less than or equal to (and/or greater than or equal to) a certain value known as a cutoff. Censoring in count data models may be dataset-defined, i.e. all values below a cutoff value are recorded as that cutoff value (left censoring), or all values above a cutoff value are recorded as that cutoff value (right-censoring). Censoring in count data models may also be observation-defined, i.e. each censored observation is described by its own left and/or right cutoff values.

The Poisson and negative binomial (NB) regression models are two of the most commonly used regression models for the analysis of discrete count data. The censored negative binomial (CNB) model is a variant of the negative binomial model that is appropriate for censored, overdispersed Poisson data. Another interesting variant of the negative binomial model involves a generalization of the overdispersion scale parameter, α, which allows for observation-specific parameterization of α. This form of the negative binomial model is known as the heterogeneous negative binomial model (HNB).

This research explored the merger of the CNB model with the HNB model to form the censored heterogeneous negative binomial (CHNB) model. Censoring in the CHNB model is either dataset-defined or observation-specific and may occur on the left, right, or on the left and right simultaneously; also, the model can accomodate interval data for which an outcome is known to be between two finite values. The research question of interest was whether the CHNB model has better performance than the HNB, CNB, and traditional NB models.

A simulation study was undertaken to assess the performance of the CHNB model in comparison to the HNB, CNB, and NB models. The simulation study incorporated the following: three sample sizes; dataset-defined censoring on the left, right, and left and right simultaneously; varying percentages of censored observations; and three sets of parameters for the heterogeneity. Models were compared based on bias, mean square error, coverage probability, Akaike Information Criterion, and Bayesian Information Criterion. The results of the simulation study show that the CHNB model performs very well in the presence of count data which includes left censoring, right censoring, and left and right censoring simultaneously, and exceeds the performances of the HNB, CNB, and NB models.

## Recommended Citation

Porter, C. N.(2011). *The Censored Heterogeneous Negative Binomial Model.* (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/553