title: Comparison of four methods for deriving hospital standardised mortality ratios from a single hierarchical logistic regression model.
abstract: There is interest in deriving case-mix adjusted standardised mortality ratios so that comparisons between healthcare providers, such as hospitals, can be undertaken in the controversial belief that variability in standardised mortality ratios reflects quality of care. Typically standardised mortality ratios are derived using a fixed effects logistic regression model, without a hospital term in the model. This fails to account for the hierarchical structure of the data - patients nested within hospitals - and so a hierarchical logistic regression model is more appropriate. However, four methods have been advocated for deriving standardised mortality ratios from a hierarchical logistic regression model, but their agreement is not known and neither do we know which is to be preferred. We found significant differences between the four types of standardised mortality ratios because they reflect a range of underlying conceptual issues. The most subtle issue is the distinction between asking how an average patient fares in different hospitals versus how patients at a given hospital fare at an average hospital. Since the answers to these questions are not the same and since the choice between these two approaches is not obvious, the extent to which profiling hospitals on mortality can be undertaken safely and reliably, without resolving these methodological issues, remains questionable.
authors.affiliation: Primary Care Clinical Sciences, University of Birmingham, Birmingham, UK m.a.mohammed@bham.ac.uk.
authors.forename: Mohammed A
authors.initials: MA
authors.lastname: Mohammed
authors.affiliation: Department of Health Sciences, University of Leicester, Leicester, UK.
authors.forename: Bradley N
authors.initials: BN
authors.lastname: Manktelow
authors.affiliation: Division of General Medicine, Veterans Affairs Ann Arbor Healthcare System and the University of Michigan Medical School, Ann Arbor, MI, USA.
authors.forename: Timothy P
authors.initials: TP
authors.lastname: Hofer
mesh_terms: D003953:Diagnosis-Related Groups; D005865:Gestational Age; D017052:Hospital Mortality; D006801:Humans; D007231:Infant, Newborn; D007363:Intensive Care Units, Neonatal; D016015:Logistic Models
keywords: Hospital standardised mortality ratios; hierarchical standardised mortality ratios; mixed-effects logistic regression; non-hierarchical hospital standardised mortality ratios