Observational studies are notoriously full of non-responses and missing values. Bayesian full
probability modelling provides a °exible 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 non-
random.
The ¯rst part of this strategy entails constructing a `base model' by selecting a model of
interest, then adding a sub-model to impute the missing covariates followed by a sub-model
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 Millennium Cohort Study
