Odds ratio (OR), relative risk (RR) (risk ratio), and absolute risk reduction (ARR) (risk difference) are biostatistics measurements that are widely used for identifying significant risk factors in dichotomous groups of subjects. In the past, they have often been used to assess simple risk factors. In this paper, we introduce the concept of compound-risk factors to broaden the applicability of these statistical tests for assessing factor interplays. We observe that compound-risk factors with a high risk ratio or a big risk difference have an one-to-one correspondence to strong emerging patterns or strong contrast sets-two types of patterns that have been extensively studied in the data mining field. Such a relationship has been unknown to researchers in the past, and efficient algorithms for discovering strong compound-risk factors have been lacking. In this paper, we propose a theoretical framework and a new algorithm that unify the discovery of compound- risk factors that have a strong OR, risk ratio, or a risk difference. Our method guarantees that all patterns meeting a certain test threshold can be efficiently discovered. Our contribution thus represents the first of its kind in linking the risk ratios and ORs to pattern mining algorithms, making it possible to find compound- risk factors in large-scale data sets. In addition, we show that using compound-risk factors can improve classification accuracy in probabilistic learning algorithms on several disease data sets, because these compound-risk factors capture the interdependency between important data attributes.