Identifying intraclass correlations necessitating hierarchical modeling

Hierarchical binary outcome data with three levels, such as disease remission for patients nested within physicians, nested within clinics are frequently encountered in practice. One important aspect in such data is the correlation that occurs at each level of the data. In parametric modeling, accounting for these correlations increases the complexity. These models may also yield results that lead to the same conclusions as simpler models. We developed a measure of intraclass correlation at each stage of a three-level nested structure and identified guidelines for determining when the dependencies in hierarchical models need to be taken into account. These guidelines are supported by simulations of hierarchical data sets, as well as the analysis of AIDS knowledge in Bangladesh from the 2011 Demographic Health Survey. We also provide a simple rule of thumb to assist researchers faced with the challenge of choosing an appropriately complex model when analyzing hierarchical binary data.