Chain Event Graphs for Informed Missingness

Abstract

Chain Event Graphs (CEGs) are proving to be a useful framework for modelling discrete processes which exhibit strong asymmetric dependence structures between the variables of the problem. In this paper we exploit this framework to represent processes where missingness is influential and data cannot plausibly be hypothesised to be missing at random in all situations. We develop new classes of models where data are missing not at random but nevertheless exhibit context-specific symmetries which are captured by the CEG. We show that it is possible to score each model efficiently and in closed form. Hence standard Bayesian selection methods can be used to search over a wide variety of models, each with its own explanatory narrative. One of the advantages of this method is that the selected maximum a posteriori model and other closely scoring models can be easily read back to the client in a graphically transparent way. The efficacy of our methods are illustrated using a cerebral palsy cohort study, analysing their survival with respect to weight at birth and various disabilities.