title: Logistic versus hierarchical modeling: an analysis of a statewide inpatient sample.
abstract: BACKGROUND
  Although logistic regression is traditionally used to calculate hospital standardized mortality ratio (HSMR), it ignores the hierarchical structure of the data that can exist within a given database. Hierarchical models allow examination of the effect of data clustering on outcomes.
  
  
  METHODS
  Traditional logistic regression and random intercepts fixed slopes hierarchical models were fitted to a dataset of patients hospitalized between 2005 and 2007 in Massachusetts. We compared the observed to expected (O/E) in-hospital death ratios between the 2 modeling techniques, a restricted HSMR using only those diagnosis models that converged in both methods and a full hybrid HSMR using a combination of the hierarchical diagnosis models when they converge, plus the remaining diagnoses using standard logistic regression models.
  
  
  RESULTS
  We restricted the analysis to the 36 diagnoses accounting for 80% of in-hospital deaths nationally, based on 1,043,813 admissions (59 hospitals). A failure of the hierarchical models to converge in 15 of 36 diagnosis groups hindered full HSMR comparisons. A restricted HSMR, derived from a dataset based on the 21 diagnosis groups that converged (552,933 admissions) showed very high correlation (Pearson r = 0.99). Both traditional logistic regression and hierarchical model identified 12 statistical outliers in common, 7 with high O/E values and 5 with low O/E values. In addition, the multilevel analysis identified 5 additional unique high outliers and 1 additional unique low outlier, and the conventional model identified 2 additional unique low outliers.
  
  
  CONCLUSIONS
  Similar results were obtained from the 2 modeling techniques in terms of O/E ratios. However, because a hierarchical model is associated with convergence problems, traditional logistic regression remains our recommended procedure for computing HSMRs.
authors.affiliation: Dr Foster Unit at Imperial College, Department of Primary Care and Public Health, Imperial College London, London, UK. r.alexandrescu@imperial.ac.uk
authors.forename: Roxana
authors.initials: R
authors.lastname: Alexandrescu
authors.forename: Min-Hua
authors.initials: MH
authors.lastname: Jen
authors.forename: Alex
authors.initials: A
authors.lastname: Bottle
authors.forename: Brian
authors.initials: B
authors.lastname: Jarman
authors.forename: Paul
authors.initials: P
authors.lastname: Aylin
mesh_terms: D003710:Demography; D017052:Hospital Mortality; D006801:Humans; D016015:Logistic Models; D008404:Massachusetts / Q000453:epidemiology; D008498:Medical Record Linkage; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods*; D011237:Predictive Value of Tests; D012959:Socioeconomic Factors