In longitudinal studies, data are collected on a group of individuals over a period of time, and inevitably
this data will contain missing values. Assuming that this missingness follows convenient `random-
like' patterns may not be realistic, so there is much interest in methods for analysing incomplete
longitudinal data which allow the incorporation of more realistic assumptions about the missing data
mechanism. We explore the use of Bayesian full probability modelling in this context, which involves
the specification of a joint model including a model for the question of interest and a model for the
missing data mechanism.
Using simulated data with missing outcomes generated by an informative missingness mechanism,
we start by investigating the circumstances and the extent to which Bayesian methods can improve
parameter estimates and model fit compared to complete-case analysis. This includes examining
the impact of misspecifying different parts of the model. With real datasets, when the form of the
missingness is unknown, a diagnostic that indicates the amount of information in the missing data
given our model assumptions would be useful. pD is a measure of the dimensionality of a Bayesian
model, and we explore its use and limitations for this purpose.
Bayesian full probability modelling is then used in more complex settings, using real examples of
longitudinal data taken from the British birth cohort studies and a clinical trial, some of which have
missing covariates. We look at ways of incorporating information from additional sources into our
models to help parameter estimation, including data from other studies and knowledge elicited from
an expert. Additionally, we assess the sensitivity of the conclusions regarding the question of interest
to varying the assumptions in different parts of the joint model, explore ways of presenting this information, and outline a strategy for Bayesian modelling of non-ignorable missing data.