McElduff, F.C.; (2012) Models for discrete epidemiological and clinical data. Doctoral thesis , UCL (University College London).

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Abstract

Discrete data, often known as frequency or count data, comprises of observations which can only take certain separate values, resulting in a more restricted numerical measurement than those provided by continuous data and are common in the clinical sciences and epidemiology. The Poisson distribution is the simplest and most common probability model for discrete data with observations assumed to have a constant rate of occurrence amongst individual units with the property of equal mean and variance. However, in many applications the variance is greater than the mean and overdispersion is said to be present. The application of the Poisson distribution to data exhibiting overdispersion can lead to incorrect inferences and/or inefficient analyses. The most commonly used extension of the Poisson distribution is the negative binomial distribution which allows for unequal mean and variance, but may still be inadequate to model datasets with long tails and/or value-inflation. Further extensions such as Delaporte, Sichel, Gegenbauer and Hermite distributions, give greater flexibility than the negative binomial distribution. These models have received less interest than the Poisson and negative binomial distributions within the statistical literature and many have not been implemented in current statistical software. Also, diagnostics and goodness-of-fit statistics are seldom considered when analysing such datasets. The aim of this thesis is to develop software for analysing discrete data which do not follow the Poisson or negative binomial distributions including component-mix and parameter-mix distributions, value-inflated models, as well as modifications for truncated distributions. The project’s main goals are to create three libraries within the framework of the R project for statistical computing. They are: 1. altmann: to fit and compare a wide range of univariate discrete models 2. discrete.diag: to provide goodness-of-fit and outlier detection diagnostics for these models 3. discrete.reg: to fit regression models to discrete response variables within the gamlss framework These libraries will be freely available to the clinical and scientific community to facilitate discrete data interpretation.

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