The Relationship Between Cluster Size, Between-Cluster Variance, and a Performance Measurement from Hierarchical Generalized Linear Models

• Activity Number: 251
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Fu-Chi Hsieh*+ and Harlan Krumholz and Zhenqiu Lin and Haiqun Lin
• Companies: Yale University, Center for Outcome Research and Evaluation and Yale University and Yale Center for Outcome Research and Evaluation and Yale University
• Keywords: Hierarchical Generalized Linear Models ; Performance Measurement ; shrinkage ; Between-Cluster Variance ; Cluster Size

Abstract

Hierarchical generalized linear modeling (HGLM) has been widely used to derive measurement for quantifying the performance of health care providers in health outcome research. Taking a provider as a cluster, the method provides cluster-specific estimates adjusted for both patients' characteristics and cluster-level random effects. Particularly, a cluster-level performance measurement, such as risk-standardized mortality rate, for a provider is calculated as average predicted probabilities (P) of death divided by average expected probabilities (E) of death. The estimates from HGLM are known as shrinkage estimates and the magnitude of shrinkage is correlated to between-cluster variance. However, the impact of shrinkage on the performance measure, a function of shrinkage estimates is still unclear. A serial of simulations was conducted for a set of realistic scenarios to investigate the relationship between the performance measure, cluster size, and between-cluster variance.

We used a hierarchical logistic model with and without covariates. The performance measure was calculated as described above. The cluster size was classified into 5 groups: < 25, 26-50, 51-150, 151-300, and > 300,