After admission to emergency department (ED), patients with critical illnesses are transferred to intensive care unit (ICU) due to unexpected clinical deterioration occurrence. Identifying such unplanned ICU transfers is urgently needed for medical physicians to achieve two-fold goals: improving critical care quality and preventing mortality. A priority task is to understand the crucial rationale behind diagnosis results of individual patients during stay in ED, which helps prepare for an early transfer to ICU. Most existing prediction studies were based on univariate analysis or multiple logistic regression to provide one-size-fit-all results. However, patient condition varying from case to case may not be accurately examined by the only judgment. In this study, we present a new decision tool using a mathematical optimization approach aiming to automatically discover rules associating diagnostic features with high-risk outcome (i.e., unplanned transfers) in different deterioration scenarios. We consider four mutually exclusive patient subgroups based on the principal reasons of ED visits: infections, cardiovascular/respiratory diseases, gastrointestinal diseases, and neurological/other diseases at a suburban teaching hospital. The analysis results demonstrate significant rules associated with unplanned transfer outcome for each subgroups and also show comparable prediction accuracy, compared to state-of-the-art machine learning methods while providing easy-to-interpret symptom-outcome information.