Some new applications of Bayesian longitudinal models.

In this dissertation we consider some novel applications of Bayesian longitudinal methods. As inference is generally focused on response of an individual, we work within the mixed model framework. The two applications are described below. Our first application is to a data set containing measurements of the probability of collision between two space objects orbiting the Earth. These measurements are longitudinal in nature, as they are observed over time and vary according to which two satellites they are taken on. This application presents a number of specific challenges, such as measurements at irregular time intervals, sparse data, and a bounded response variable. The second application is that of longitudinal network meta-analysis. In clinical trials, one major question is how to compare treatments across trials. However, current methods usually only deal with comparisons at a single time point, discarding data at other time points. This problem presents different challenges from the previous, such as defining network treatment effects over time, developing diagnostic methods for choosing a correct model, and dual longitudinal models for the mean and variance.