When patient data are shared for studying a specific disease, a privacy disclosure occurs as long as an individual is known to be in the shared data. Individuals in such specific disease data are thus subject to higher disclosure risk than those in datasets with different diseases. This problem has been overlooked in privacy research and practice. In this study, we analyze disclosure risks for this problem and identify appropriate risk measures. An efficient algorithm is developed for anonymizing the data. An experimental study is conducted to demonstrate the effectiveness of the proposed approach.