Bayesian Belief Networks (BBNs) play a relevant role in the field of Artificial Intelligence in Medicine and they have been successfully applied to a wide variety of medical domains. An appealing character of BBNs is that they easily extend into a complete decision-theoretic formalism known as Influence Diagrams (IDS). Unfortunately, BBNs and ros require a large amount of information that is not always easy to obtain either from human experts or from the statistical analysis of databases. In order to overcome this limitation, we developed a class of IDs, called Ignorant Influence Diagrams (IIDs), able to reason on the basis of incomplete information and to to improve the accuracy of the decisions as a monotonically increasing function of the available information. The aim of this paper is show how IIDs can be useful to model medical decision making with incomplete information.