Prediciton regions for the visualization of incomplete datasets

Abstract

A complication in the visualization of biomedical datasets is that they are often incomplete. A response to this is to multiply impute each missing datum prior to visualization in order to convey the uncertainty of the imputations. In our approach, the initially complete cases in a real-valued dataset are represented as points in a principal components plot and, for each initially incomplete case in the dataset, we use an associated prediction region or interval displayed on the same plot to indicate the probable location of the case. When a case has only one missing datum, a prediction interval is used in place of a region. The prediction region or interval associated with an incomplete case is determined from the dispersion of the multiple imputations of the case mapped onto the plot. We illustrate this approach with two incomplete datasets: the first is based on two multivariate normal distributions; the second on a published, simulated health survey.