title: Fixed effects modelling for provider mortality outcomes: Analysis of the Australia and New Zealand Intensive Care Society (ANZICS) Adult Patient Data-base.
abstract: BACKGROUND
  Risk adjusted mortality for intensive care units (ICU) is usually estimated via logistic regression. Random effects (RE) or hierarchical models have been advocated to estimate provider risk-adjusted mortality on the basis that standard estimators increase false outlier classification. The utility of fixed effects (FE) estimators (separate ICU-specific intercepts) has not been fully explored.
  
  
  METHODS
  Using a cohort from the Australian and New Zealand Intensive Care Society Adult Patient Database, 2009-2010, the model fit of different logistic estimators (FE, random-intercept and random-coefficient) was characterised: Bayesian Information Criterion (BIC; lower values better), receiver-operator characteristic curve area (AUC) and Hosmer-Lemeshow (H-L) statistic. ICU standardised hospital mortality ratios (SMR) and 95%CI were compared between models. ICU site performance (FE), relative to the grand observation-weighted mean (GO-WM) on odds ratio (OR), risk ratio (RR) and probability scales were assessed using model-based average marginal effects (AME).
  
  
  RESULTS
  The data set consisted of 145355 patients in 128 ICUs, years 2009 (47.5%) & 2010 (52.5%), with mean(SD) age 60.9(18.8) years, 56% male and ICU and hospital mortalities of 7.0% and 10.9% respectively. The FE model had a BIC = 64058, AUC = 0.90 and an H-L statistic P-value = 0.22. The best-fitting random-intercept model had a BIC = 64457, AUC = 0.90 and H-L statistic P-value = 0.32 and random-coefficient model, BIC = 64556, AUC = 0.90 and H-L statistic P-value = 0.28. Across ICUs and over years no outliers (SMR 95% CI excluding null-value = 1) were identified and no model difference in SMR spread or 95%CI span was demonstrated. Using AME (OR and RR scale), ICU site-specific estimates diverged from the GO-WM, and the effect spread decreased over calendar years. On the probability scale, a majority of ICUs demonstrated calendar year decrease, but in the for-profit sector, this trend was reversed.
  
  
  CONCLUSIONS
  The FE estimator had model advantage compared with conventional RE models. Using AME, between and over-year ICU site-effects were easily characterised.
authors.affiliation: Department of Intensive Care Medicine, The Queen Elizabeth Hospital, Woodville, South Australia, Australia.
authors.forename: John L
authors.initials: JL
authors.lastname: Moran
authors.affiliation: School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia, Australia.
authors.forename: Patricia J
authors.initials: PJ
authors.lastname: Solomon
mesh_terms: D000328:Adult; D000368:Aged; D001315:Australia; D003422:Critical Care / Q000706:statistics & numerical data*; D016208:Databases, Factual; D005260:Female; D006282:Health Personnel / Q000706:statistics & numerical data*; D006761:Hospitals / Q000706:statistics & numerical data; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D009026:Mortality; D009520:New Zealand