Bayesian methods for modelling non-random missing data mechanisms in longitudinal studies

Abstract

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.