title: Approximate models for aggregate data when individual-level data sets are very large or unavailable.
abstract: In this article, we study a Bayesian hierarchical model for profiling health-care facilities using approximately sufficient statistics for aggregate facility-level data when the patient-level data sets are very large or unavailable. Starting with a desired patient-level model, we give several approximate models and the corresponding summary statistics necessary to implement the approximations. The key idea is to use sufficient statistics from an approximate model fitted by matching up derivatives of the models' log-likelihood functions. This derivative matching approach leads to an approximation that performs better than the commonly used approximation given in the literature. The performance of several approximation approaches is compared using data on 5 quality indicators from 32 Veterans Administration nursing homes.
authors.affiliation: Boston University School of Management, 595 Commonwealth Avenue, Boston, MA 02215, U.S.A. pekoz@bu.edu
authors.forename: Erol A
authors.initials: EA
authors.lastname: Peköz
authors.forename: Michael
authors.initials: M
authors.lastname: Shwartz
authors.forename: Cindy L
authors.initials: CL
authors.lastname: Christiansen
authors.forename: Dan
authors.initials: D
authors.lastname: Berlowitz
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D019985:Benchmarking / Q000706:statistics & numerical data; D003198:Computer Simulation; D006268:Health Facilities / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009735:Nursing Homes / Q000706:statistics & numerical data*; D016012:Poisson Distribution; D019984:Quality Indicators, Health Care / Q000706:statistics & numerical data; D011787:Quality of Health Care / Q000706:statistics & numerical data*; D020379:Risk Adjustment; D014481:United States; D014493:United States Department of Veterans Affairs