We develop a robust ranking procedure to uncover trends in variation in antibiotic resistance (AR) rates across hospitals for some antibiotic-bacterium pairs over several years. We illustrate how the method can be used to detect potentially dangerous trends and to direct attention to hospitals' management practices. A robust method is indicated due to the fact that some unusual reported resistance rates may be due to measurement protocol differences and not any real difference in AR rates. Our proposed method is less sensitive to outlier observations than other robust methods. The application on real AR data shows how a dangerous trend in a particular AR rate would be detected. Our results indicate the potential benefits of systematic AR rate collection and AR reporting systems across hospitals.