Sensitivity analysis for incomplete categorical data

Classical inferential procedures induce conclusions from a set of data to a population of interest, accounting for the imprecision resulting from the stochastic component of the model. This is usually done by means of precision or interval estimates. Less attention is devoted to the uncertainty arising from (unplanned) incompleteness in the data, even though the majority of clinical studies suffer from incomplete follow-up. Through the choice of an identifiable model for non-ignorable non-response, one narrows the possible data generating mechanisms to the point where inference only suffers from imprecision. Some proposals have been made for assessment of sensitivity to these modelling assumptions; many are based on fitting several plausible but competing models. We propose a formal approach which identifies and incorporates both sources of uncertainty in inference: imprecision due to finite sampling and ignorance due to incompleteness. The developments focus on contingency tables, and are illustrated using data from a HIV prevalence study and data from a psychiatric study.