Missing Data Methodology: Sensitivity analysis after multiple imputation

Within epidemiological and clinical research, missing data are a common issue which are often inappropriately handled in practice. Multiple imputation (MI) is a popular tool used to `fill in' partially observed data with plausible values drawn from an appropriate imputation distribution. Software generally implements MI under the assumption that data are `missing at random' (MAR) i.e. that the missing mechanism is not dependent on the missing data conditional on the observed data. This is a strong inherently untestable assumption, and if incorrect can result in misleading inferences. The sensitivity of inferences to this assumption needs to be assessed by exploring the alternative assumption that missing data are `missing not at random' (MNAR) i.e. even conditioned on the observed data, the probability of missing observations depends on their unseen, underlying values. Broadly there are two ways to frame, and perform sensitivity analyses (SA) to accomplish this: using a pattern mixture model or a selection model. Motivated by a cancer dataset, we develop a novel pattern mixture approach to collecting and incorporating in the analysis prior information elicited from experts. We demonstrated the inferential validity of our approach by simulation. Our second example is an individual patient meta-analysis of sudden infant death syndrome studies. We extended existing multilevel MI software to perform SA for the risk of bed sharing in these complex data. Inferences were found to be robust. Finally we considered a proposal of Carpenter et al. (2007) for SA after MI by reweighting. We developed a modification, which dramatically improves its performance in small data sets. The routine use of SA in applied research is held back by the lack of practical methodology and examples. This thesis addresses these issues, and so lowers the barrier to the widespread adoption of SA.