Sample size considerations in observational health care quality studies

A common objective in health care quality studies involves measuring and comparing the quality of care delivered to cohorts of patients by different health care providers. The data used for inference involve observations on units grouped within clusters, such as patients treated within hospitals. Unlike cluster randomization trials where often clusters are randomized to interventions to learn about individuals, the target of inference in health quality studies is the cluster. Furthermore, randomization is often not performed and the resulting biases may invalidate standard tests. In this paper, we discuss approaches to sample size determination in the design of observational health quality studies when the outcome is binary. Methods for calculating sample size using marginal models are briefly reviewed, but the focus is on hierarchical binomial models. Sample size in unbalanced clusters and stratified designs are characterized. We draw upon the experiences that have arisen from a study funded by the Agency for Healthcare Research and Quality involving assessment of quality of care for patients with cardiovascular disease. If researchers are interested in comparing clusters, hierarchical models are preferred.