The Australian and New Zealand Intensive Care Society Adult Patient Database (ANZICS APD) is one of the largest databases of its kind in the world and collects individual admissions data from intensive care units (ICUs) around Australia and New Zealand. Use of this database for monitoring and comparing the performance of ICUs, quantified by the standardised mortality ratio, poses several theoretical and computational challenges, which are addressed in this paper. In particular, the expected number of deaths must be appropriately estimated, the ICU casemix adjustment must be adequate, statistical variation must be fully accounted for, and appropriate adjustment for multiple comparisons must be made. Typically, one or more of these issues have been neglected in ICU comparison studies. Our approach to the analysis proceeds by fitting a random coefficient hierarchical logistic regression model for the inhospital death of each patient, with patients clustered within ICUs. We anticipate the majority of ICUs will be estimated as performing usually after adjusting for important clinical covariates. We take as a starting point the ideas in Ohlssen et al and estimate an appropriate null model that we expect these ICUs to follow, taking a frequentist rather than a Bayesian approach. This methodology allows us to rigorously account for the aforementioned statistical issues and to determine if there are any ICUs contributing to the Australian and New Zealand Intensive Care Society database that have comparatively unusual performance. In addition to investigating the yearly performance of the ICUs, we also estimate changes in individual ICU performance between 2009 and 2010 by adjusting for regression-to-the-mean.