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Abstract

Drop-outs are a common problem in longitudinal studies. In terms of statistical models for the data, there are three types of drop-out mechanisms: drop-out occurring completely at random (CRD), drop-out occurring at random (RD) and informative drop-out (ID). The drop-out mechanism is classified as CRD if the drop-out mechanism is independent of the measurements; as RD if the drop-out mechanism depends only on the observed but not the unobserved measurements, and as ID if the drop-out mechanism depends on both the observed and unobserved measurements. CRD and RD are referred to as ignorable because the drop-out mechanism can be ignored for the purpose of making inferences about the observed measurements, while ID is non-ignorable. Analyses based on an assumption of ignorable drop-out, when in reality the drop-out mechanism is non-ignorable, can lead to misleading or biased results. Likelihood-based models for continuous and categorical longitudinal data subject to non-ignorable drop-out have been developed. In this thesis, we focus on exploring likelihood-based models for binary longitudinal data subject to informative drop-out. The two modelling approaches considered are a selection model proposed by Baker (1995) and a transition model proposed by Liu et al. (1999). We apply these models to a data set from a multiple sclerosis (MS) clinical trial. The aims of the analyses are to investigate whether there is an indication of informative drop-out in this data, and to assess the sentivity of inferences concerning the treatment effects to the underlying drop-out mechanisms. We do not attempt to provide a definitive analyses of the data set, but rather to explore a variety of models which incorporate informative drop-out.