Strategy for Modelling Nonrandom Missing Data Mechanisms in Observational Studies Using Bayesian Methods

Observational studies inevitably suffer from nonresponses and missing values. Bayesian full probability modelling provides a flexible approach for analysing such data, allowing a plausible model to be built which can then be adapted to carry out a range of sensitivity analyses. In this context, we propose a strategy for using Bayesian methods for a "statistically principled" investigation of data which contains missing covariates and missing responses, likely to be nonrandom. The first part of this strategy entails constructing a "base model" by selecting a model of interest, then adding a submodel to impute the missing covariates followed by a submodel to allow informative missingness in the response. The second part involves running a series of sensitivity analyses to check the robustness of the conclusions. We implement our strategy to investigate some typical research questions relating to the prediction of income, using data from the UK Millennium Cohort Study. © Statistics Sweden.