Inter-unit reliability for nonlinear models

In monitoring dialysis facilities, various quality measures are used in order to assess the performance and quality of care. The inter-unit reliability (IUR) describes the proportion of variation in the quality measure that is due to the between-facility variation. If the measure under evaluation is a simple average across normally distributed patient outcomes for each facility, the IUR is based on a one-way analysis of variance (ANOVA). However, more complex quality measures are not simple averages of individual outcomes. Even the standard bootstrap methods are inadequate because the computational burden increases quickly as the sample size grows, prohibiting its application in large-scale studies. To generalize the IUR to complex quality measures used in nonlinear models, we propose an approach combining the strengths of ANOVA and resampling. The proposed method is computationally efficient and can be applied to large-scale biomedical data with complex data structures. The method is exemplified in various measures of dialysis facilities using national dialysis data.