Predicting an individual's risk of getting a stroke has been a research subject for many authors worldwide since it is a frequent illness and there is strong evidence that early awareness of having that risk can be beneficial for prevention and treatment. Many Governments have been collecting medical data about their own population with the purpose of using artificial intelligence methods for making those predictions. The most accurate ones are based on so called black-box methods which give little or no information about why they make a certain prediction. However, in the medical field the explanations are sometimes more important than the accuracy since they allow specialists to gain insight about the factors that influence the risk level. It is also frequent to find medical information records with some missing data. In this work, we present the development of a prediction method which not only outperforms some other existing ones but it also gives information about the most probable causes of a high stroke risk and can deal with incomplete data records. It is based on the Dempster-Shafer theory of plausibility. For the testing we used data provided by the regional hospital in Okayama, Japan, a country in which people are compelled to undergo annual health checkups by law. This article presents experiments comparing the results of the Dempster-Shafer method with the ones obtained using other well-known machine learning methods like Multilayer perceptron, Support Vector Machines and Naive Bayes. Our approach performed the best in these experiments with some missing data. It also presents an analysis of the interpretation of rules produced by the method for doing the classification. The rules were validated by both medical literature and human specialists.